Please accept my apology for the delay in getting back to you on this. You can rest assured that I have not been ignoring the questions, in fact, quite the contrary is true. Not only have I been repeatedly looking at this problem, I actually copied the photos and pasted them in my photo editing program where I enlarged them about ten times to get a closer look. Now let me share what I have concluded and see if it corresponds to what you have found. Fact- The house is only 6 years old so all work should conform to the codes that are currently in force. Fact-The T&P valve drain line, Water heater drip pan & HVAC condensate drain line must either terminate outside the structure or discharge into an approved indirect waste receptor. Fact-the T&P drain line may not discharge into the drip pan and the T&P drain line & drip pan drain line MAY NOT be connected to a common drain line. FACT-The T&P drain line, drip pan drain line & HVAC condensate drain line must run "Full Bore" from the source to the point of discharge. From my observation of the photos- The 1-1/2" line extends out from the wall then turns upwards by means of a 1/4 bend with a 3" x 1-1/2" reducer bushing and a short section of 3" pipe that probably was about 4" to 6" high, which would create a waste receptor for the T&P drain & HVAC condensate All of the joint on that section of the line show clear evidence of PVC cleaner/solvent with purple dye. All of that work was probably originally done during the initial "Stack out phase" of the plumbing. At that time the walls would have still been open and the full length of that run would be open for inspection. Now here is my first dilemma. Code expressly prohibits downsizing a DWV line in the direction of flow and that would have immediately caught the inspectors eye. Once the inspector realized that the short section of 3" pipe was intended as a receptor for the T&P drain, Pan drain & HVAC condensate line he/she would have classified that 3" as a fixture and would have then checked closely to see where the 1-1/2" waste arm was discharging. If the 1-1/2" line was connected to the DWV system the inspector would have insisted on a trap under the receptor. The lack of a trap suggests that the line is running to the nearest exterior wall and discharging outdoors, which would not require a trap. There is an extremely remote possibility that they installed a trap in the wall as you suggest, however code only permits a maximum of 15" horizontal offset from the fixture drain opening to the trap input; and it appears that the distance from the 1/4bend to the wall is very close to that length. Why would they put the trap in the wall if it could be much easier attached under the receptor on the end of the line where the 1/4 bend is? It is possible that with the trap on the end of the line it would have exceeded the maximum allowable length from the trap weir to the vent opening for an 1-1/2" line (see my post on "Fixture arm defined") so they installed a trap in the wall and attached the horizontal offset to extend the line, but you said that the drain line in the adjoining bathroom is close therefore this simply defies logic. Now here is the problem at hand. If that line discharges outside the structure as I suspect you cannot attach your water treatment discharge line to that line. On the other hand, if that line is attached to the DWV system you must first determine if there is a trap in the wall because code requires a trap for all fixtures attached to the DWV system. You may not just arbitrarily attach a trap as you suggest because code expressly prohibits "Double trapping" (having two traps in series). In fact, years ago all structures were required to have a "House Trap" on the main sewer line where it attaches to the house main drain, but those traps are now outlawed under the no double trapping rule. Now for the other discrepancies noted: Examine the connections where the T&P discharge line, HVAC condensate line and the water heater drip pan are attached. Note that there is no evidence of purple dye on the joints. This suggests to me that those lines were installed by someone else after the original waste receptor was installed and the individual who made those connections was not familiar with code requirements. Note that the HVAC drain line is a 3/4" PVC line and they attached a 3/4" tee to accept the discharge end of the T&P drain line. That is a code violation. Properly to combine both the HVAC drain and the T&P discharge line that MUST BE a 1" Tee. Under the top tee there is a 3/4"x1" bushing increasing the line to 1" to receive the 1" discharge line from the drip pan. At minimum that tee must be 1-1/4". It also appears that in the process of connecting the drip pan drain line they had to cut the 3" down flush with the reducer on the 1-1/2" quarter bend therefore you no longer have a receptor. Properly the 1-1/2" line should have been a bit lower, but lacking that, the water heater should have been raised up on bricks or other suitable supports to allow vertical clearance for the drip pan line into the receptor. You also stated that the only line visible outside the structure is a cleanout, which is 30' from the building. Code requires that on slab construction the Main Cleanout must be at the junction of the house main drain and house sewer within 3' of the footer wall. I suspect you main cleanout may be slightly covered with dirt and not visible and the cleanout that you found is at a change in direction of the house sewer. Code requires on a house sewer we must have a cleanout at any change of direction which is 45deg or greater and one for every 80 linear 80' of run. As much as I hate to say it, in my humble opinion the only sure way to resolve the issue here would be to make a small opening in the wall and physically see if the line in question is attached to the DWV system and insure whether or not there is a trap. BUT,there is a metal perf strap securing the line to the wood blocking behind the 1/4bend. Code expressly prohibits using metal hangers on plastic pipe. The copper T&P discharge line is discharging into the top of a 3/4" PVC tee from the HVAC condensate line. Under the Tee there is a 3/4"x1" bushing which is enlarging the line to 1" before it enters the 1" tee from the drip pan.

I agree it's hard to give a fair answer without knowing the layout/seeing photos and understanding the reasons why DH and others suggest combining. With that said, the big negative, for me, would be the noise. Our laundry is in an adjacent room to the kitchen/living room and it's hard to hear the TV/each other with the laundry running. Being able to close a door on that sound is a big help. If you can manage to only do laundry at off times, I guess that wouldn't matter. The second negative depends on how you do laundry. Do you have dirty clothes sitting around in the laundry space? If so, I would opt to isolate that mess/dirt/smell in another space. We are childless so we don't collect laundry in our laundry room.... so, that wouldn't be an issue for us/everyone but it's something to consider. The positives, potentially, are a larger feel to your kitchen..... and more countertop space. What are the positives your DH sees?

My laundry room is only that; it's not a mud room or utility room. I have lots of shelves - hub built most of them and installed them. There are huge hooks he installed for me to hang clothes on (I hang and fold clothes as I'm taking them out of the dryer). He also installed a nice rod/shelf above the dryer so that I can hang or lay things there to air dry. Other than machines, hooks on the wall, and shelves, I have lots of laundry detergent, a jug of vinegar, a huge jug of fabric softener (one lasts more than a year), a box of OxiClean and Color Catchers for when I combine colors in a load (I don't do that often, but I have a thing about only washing full loads). And a tall kitchen size trash can which seems to stay full - I haven't figured that out yet. Mine is very utilitarian, but it works for me and is in a very handy location.

"It might not be strictly to code to hide these things" Does that mean it's allowed, or not allowed? Plumbing and electrical codes exist for safety under broadly accepted standards, not as choices to make. So that future owners and occupants know that work was done in compliance with such standards and that emergency access meets requirements. When doing a remodel with building permits, we wanted to put a panel on a wall that would be behind a door when it was opened. That wasn't allowed. "water heater but it's no less accessible than it was before.." Clearance past the washer - in photo #2, nearly three tiles wide. In photo #4, less than the width of one tile.