A back panel is not really required in lower cabinets. It really doesn’t do anything that can’t be done by stretchers. This is even more true for drawer stacks.

I would assume that the cabinetmaker is going to use a bottom stretcher to prevent things from being pushed out the gap in back.

Typically, any cabinet that is near eye level or shallow would get a back panel. Structurally a stretcher is sufficient but it looks unfinished and is not something I have ever seen in a kitchen. I would not accept upper cabinets without a back panel.

Lower cabinets that have to be shimmed off the out of whack wall will now have a hollow behind them, open to the toekick area. Nothing may end up falling down in there, but that depends on what you store there.

I would not accept these cabinets as being what most people would assume as "custom". Custom is not the same thing as quality.

This is a case of what's necessary vs preferable. As the others mentioned with stretchers structurally they'll likely still be fine, but when you open it and look inside there will likely be a gap at the back that will be visible. However, if these are all going to be drawer bases then that may not matter to you. Regardless, should be very easy for the builder to rip some 1/4" MDF to glue in as backs.

There shouldn’t be a gap in the bottom back. Everyone who builds cabinets like this is going to put the back stretcher at the cabinet bottom.

This subject comes up regularly on this forum. Backing on lower cabinets just is not necessary. Not even aesthetically because you really never see the backing on a lower cabinet anyway. Especially on drawer stacks.

I did one kitchen with custom cabinets by Wood-mode and one with custom cabinets by a local cabinet company. Both had full back for upper and lower cabinets and drawer stacks.

Custom made lower cabinets didn't traditionally have back panels. They were largely added to counter shipping problems in mass produced cabinetry.

A good quality cabinet is going to have stretchers even if it has a back panel, you don't want a large panel on the back of the cabinet, as it just makes the install worse. Adding a back panel just removes 1/4" to a 1/2" of useable space and gives you what you expect to see.

Technically, the same happens with uppers, they just remove cabinet space and add no real stability or advantage. However, since uppers are not as deep and they are at eye level, they typically have backs for aesthetic reasons. This doesn't say anything about the quality of cabinet construction really. Even uppers without backs don't say anything about cabinet quality, but they will certainly be perceived as being lower quality and perception does matter when it is that obvious.