I'm sorry, but I'm having a hard time understanding why the constraints are contradictory. For example, can't you just have a thin countertop such that the corner is within 18 inches of the edge and put an outlet there?
So first of all, 18 inch counters are a little cramped, so this regulation means that nobody gets a counter big enough to have small appliances or ingredients containers and still has space to put a cutting board or roll dough in front of it.
I think it depends on how the code deals with corners. If 18 inches apart means that I can have the first outlet 18 inches from a corner, then I might be okay, or I might have to make 15-16 inch deep counters so that you can reach it even though it's right near the elbow.
If the 18 inches means I have to place outlets 9 inches from the corner, then you can't reach them. Or if you can convince them that Pythagoras was an okay guy and 12.75" from the corner is fine because 2 * 12.75^2 ~= 18^2, I'm still not quite able to reach those outlets unless I make a kitchen with crazy shallow counters.
The only other options involve chopping up the counter top into alcoves with the outlets set forward, including filling in the corner of the L. Otherwise you have to move the outlets away from the walls, which means not only are cords dangling all over your kitchen, but they're being exposed to fluids, either of which is so stupid that it should be against code but probably isn't.
I think the implication from OP is that effectively the only sane reaction is to build galley kitchens, (which might be better for people on canes or crutches, but would be difficult for people in chairs, and generall suck for everybody), or to build the oven or microwave into the corner to fill the space and/or give a reasonable spot to put an outlet.
But both of those essentially destroy the value of the corner, which is to house an arbitrarily large countertop appliance of your choosing, such as a juicer, dehydrator, or commercial grade stand mixer. And with 18 inch counter depth regulations you're sure as fuck gonna need it.
Most of my countertop is much narrower than 18" because of cabinets going down to the surface. This is only a problem because they don't want to put something in place that breaks up the L-shape, such as a cabinet.
As noted above, corners are utilized for storing large items that don't otherwise fit comfortably on the counter.
In my own kitchen, the corner is used to store a mid-size toaster over. There is still plenty of room in front of the oven to butter toast or other smaller cooking tasks.
Take away the corner and my toaster is now moved to a straight piece of counter, where is takes all of the depth when open, and with no room in front to butter my toast.
This is a simple case of putting the needs of the few ahead of the many. I'm all for accessible public spaces, but why should my home be required to be built in such a way that it is less useful to me?
I honestly don't think I could work in your kitchen. :P I have 24" counters for the most part, with a few places that go to 36" because they are open on both sides. My mom's house has 18" counters, and I have a real hard time cooking in her kitchen. They're barely usable with all the stuff on them, though they wouldn't be too bad if they were clear.