Nope! In fact, I run mine with a Dvorak layout by default. A lot of people who use the QMK firmware do all kinds of custom modifiers, macros, and what not. And if you're doing your own PCB, you can arrange the buttons any way you want, with any switch type.
You could make it whatever shape you want. Then program it to emit whatever usb key codes you want (there are existing libraries to do this quite easily).
This one happens to emit standard qwerty key codes, but there are many more that do other things. For example, there are standard key codes to launch a browser or the calculator (and some keyboards have buttons to do that too). You could also make it emulate any kind of standard usb HID (human interfact device). This one is a keyboard, but you could make something that identifies itself as a mouse, game controller, etc.
My Ergodox is configured so that hitting a particular key switches hjkl to mouse control, with clicks on the other hand. I can’t say I use it often, but it’s nice for times when you just want to click a single thing and then get back to typing.
you aren't limited to QWERTY but there are some limitations in what you can send from a USB keyboard. Depending on what you're trying to accomplish you might want to do some of it in the keyboard and part on the computer using AutoHotkey/Hammerspoon.
What I’m thinking about is to actually make a custom physical user interface. Less of a keyboard and more the bridge of USS Enterprise.