I can't imagine that this change could cost that much money. Move forward if this is what you really want. If it were me I would leave it alone unless you have extra funds to pay for the additional work that may be required. Good luck and hope it all comes out the way you want!

Your plumbing vent as well as electrical is located in that wall. You will have to relocate that to inside the cabinets. The venting is especially bulky if you have an island loop vent. I suggest that you open that drywall up now and figure out what is in there during the design phase.

Or just cover the drywall with cabinet panels as is fairly standard. And don’t use a blind corner cabinet. There are way to many other choices that are far better!

You will have to most likely relocate drain line, vent line, branch piping and electrical outlet that is located inside that wall you are planning to remove. I would figure out the cost of making these changes and whether it is that important for you. Sometimes in construction you have to make some sacrifices so just depends what you are willing to sacrifice- money or the design.

You may not be able to cut that wall down at all. Your vent runs through it. You need a good plumber who has a relationship with the local inspector. Some would immediately red tag that. And you can not do this without a permit!

I’m not quite sure what you mean by “punching out” a cabinet, but I could see shallow depth cabinets in place of the pony wall behind the peninsula instead. I can’t see why it can’t be done without moving any plumbing. Electrical outlet would need to be moved. The new cabs might need to have a couple of holes put in them for the water lines to run through, but nothing else plumbing would need to be moved.

It's more than supply lines. Supply lines are easy and small and use water pressure to work.

The drain and vent runs through that wall. They are large and bulky. Drains and vents use gravity and air pressure.

There are big rules about slopes for drains so that they do drain. And for vents so that deadly sewer gas does not end up in your house.

All of that would need to be redone if that wall went away. And possibly if it were even shortened. Which is why the plumber and the permit are needed.

GreenDesigns, in the undersink picture it looks like all the drain lines run under the current cabinet to the “wall”. I’m not sure if the OP meant the pony wall or the end of the peninsula where it meets the wall base cab, but again, the new cabs would back up to that. Maybe a part of the drainage might have to be accommodated for with the new cabs, but it doesnt seem to be a major construction project.

Sorry, but you don't understand plumbing. It is not trivial or minor surgery. Removing that wall is 100% redoing every bit of plumbing in that wall after new cabinets go in, which makes it even more difficult. No, it's not plumbing the whole house. But it's not a 5 minute hook up either. And won't be priced like that either.

In order to gain access to the blind corner, do you mean to create an opening in the wall and punch into the existing corner cab? I don't see how you need to mess with the sink cabinet, unless you want to have doors accessing all cabinets along that peninsula. Here's what we did to make better use of the corner cabinet space (it's also accessible from other side; we store trays in there now)

We had a local crafstman build this shelf insert and cut into the cabinet & peninsula skin (old photo: tiling/painting complete now)