Has anyone tried to live by only cooking out of an electric pressure cooker? I've never had one, but they appear to function like a pot on the stove if you take the lid off. Is this a bad idea? Should I plan on having a cooktop as well?
I've got an 8qt Instant Pot we use quite a bit (should be about the same as any other electric pressure cooker), and, yes, you should be able to use them like a pot if you take the lid off. A lot of the stuff we do will have us brown the meat first (with the lid off), then throw everything in and let it heat up. I'm not sure you'd want a 10qt, though. I have an 8qt, and it's quite large (I can do doubles of most recipes in it), but it doesn't do small stuff very well. I can cook a cup of rice in it, but... eh. It's a very, very thin layer of rice I end up having to scrape off the bottom at that point. For one or two people, the 6qt is probably about right (I bought larger than currently needed because we've got 2 kids who, hopefully well within the lifespan of this unit, will be teenagers who inhale everything in sight and a lot of stuff that isn't).
They also can work as a slow cooker.
I would miss a stovetop for our cooking, but we live in a house with plenty of space and, admittedly, most of my cooking has been on a stove so that's what I'm used to. I think, if I really had to, I could do most of my cooking with the Instant Pot, and if I only had one, I'd certainly change my eating around to focus on what it works well for.
In your case, I'd probably design without a stovetop. You can always get a countertop induction burner if you find you can't live without it. Devoting counter space to a cooktop, unless you're going with a gas one, probably doesn't make sense.
... how
are you powering all this stuff? Shore power?