If you want to run a washing machine attached only to a cold water feed, you can do that by buying one of the handful of 240 volt washers sold in the US, mainly from Bosch or Asko. I have a Bosch 240v washer and the owner's manual specifically states it can be attached to cold water only, although you'll need a Y-adapter for the water line to physically send cold water to both the hot and cold inlets on the washer. I don't know without looking if the Asko 240v units are designed this way; I know Miele allowed cold-only water use before they switched most of their US-market washers to 120v. All of the currently available 240v washers are the more compact 24" width rather than the more common 27", so they don't hold as much as the monster-sized washers that have become popular in recent years. They do hold as much as a typical '80s or '90s top-load washer though; the recently introduced Bosch 240v washers claim to be able to handle a 17-1/2 lb. load, which is about what old top-loaders could fit. The water heaters in 240v washers are typically 2000 to 2500 watts compared to 1000 watts in a 120v machine, which is inadequate for heating cold water without taking an inordinate amount of time. Even the 240v washers will have somewhat longer wash cycles when running on cold water. A side benefit is that filling with cold water will help prevent some types of stains from becoming permanent.

Tankless heaters have used as a marketing idea that they will increase efficiency by not having hot water sitting around in a tank all day not being used. It's an easy concept for consumers to grasp, but it's not true. On an electric heater, the difference in the energy factor is very small between a tank and a tankless heater. A tank heater will be in the area of 0.93 and a tankless might be 0.95 - not enough difference to talk about and certainly not enough to provide payback. That represents the amount of heat lost through the walls of a well insulated tank. With gas heaters it's different. The vast majority of the efficiency gain is in the lowered flue temps. Second is not having the heat loss through the center of the tank. For your situation, what you should know is that a properly installed and operating electric tank heater is extremely reliable and efficient. Get yours replaced or repaired and the TPV properly routed to the drain so that it doesn't cause damage. Since you have lost confidence in your heater, I would just replace it rather than repair. Make sure that you are addressing thermal expansion issues that might have caused the TPV to open. If you want more space, consider a stacking washer and dryer and eliminating the sink. The front loading LG's are full size (huge inside) stack and don't use much water - eliminating the overflowing washtub issue. That would be a cheaper way to get space than a tankless heater and they are great machines.

"I've considered the systems that use the cold water line as a return. There are some concerns about mixing hot water in the cold water lines, since it is not recommended to drink water from the hot side". The amount of water from the hot side pumped into the cold side is diluted and therefore not the same as drinking hot water. "The main concern is legionnaires disease, but others worry about the increased solubility of minerals and other compounds". My wife is an ICP and assured me that the anti-bacterials (chlorine or the like) added in the cold water by our water utility continue to work at a temperature a few degrees over its normal temp and that those same anti-bacterials (chlorine or the like) work just as well in the water heater where the temp is considerably higher than the cold water. I would consider a well water system an entirely different environment since the water is not necessarily safe when pumped from the ground. I can see where Chris8796 would make that statement never having experienced the device in question so here are facts not unsubstantiated opinions... The Laing Autocirc and the Watts version retrofit recirc pumps are NSF certified and not prohibited by any code I can find in the US. This link http://lainginc.itt.com/pdf/ACT303Brochure_web.pdf to the Autocirc brochure lists it's certifications. Living with the Autocirc for 7+ years I never find the temp of the water on the cold side of the sink where the pump is installed to be much above the normal temp of the cold water so any increased solubility is not a consideration and note that no other faucet between the far sink with the device and the WH connects hot and cold. " also got a chuckle from their marketing, "the average family of 4 saves 43 gallons of water a day"? A 3/4" copper pipe holds 0.025 gallons per linear foot and a 1/2" copper pipe holds 0.0121 gallons per linear foot, 43 gallons would fill 1720 feet of 3/4" or 3553 feet of 1/2" pipe. Now, thats a long from the water heater, even if you had to use water 10 times a day". With just two people in a 1600 sq ft home we hit a faucet or appliance far more often than ten times a day and factor in the two plus minutes we used to let the hot water run till it was hot and Laing's claims are in the ballpark. Here are the facts in my first hand experience... no opinion, just fact. My water meter ticks over each 1000 gallons. My average water usage was 4000 gallons per month and every 5th month or so it would drop to 3000 gallons on one months bill then back up to 4000 gallons. With the Laing Autocirc installed the monthly bills dropped to 3000 gallons for four months and then one month at 4000 gallons. That savings coupled with the savings in KCl for my softener (less water used, less softening needed, less KCl used), less LP used to heat the water, and having hot water at the kitchen sink in seconds was a win-win all the way around.

Some washers with onboard water heating are time-limited in how long the wash period is held/extended while the heater operates. The intended target temp for some cycles may not be reached if the initial fill is not hot enough per the machine's engineered/design parameters. Designated Sanitary cycles typically have longer hold times but still may fall a little short of the target. I used a 2006 Whirlpool Duet HT for a couple months. The Whitest Whites cycle and Heavy cycle (on both warm and hot temp settings) utilized the heater but only on the highest soil level. I ran a few loads on both warm and hot with cold and warm-er and hot-ish fills to test the effect of heating, and found that the end-result wash temp fell further short of the expected "warm" or "hot" target with cooler initial fills. The Sanitary cycle had a much longer heating period and seemed to always reach the target if the initial fill was at least warm.