A mapping such as map super+h previous_window doesn't override the system's Hide shortcut, so pressing command+h hides Kitty. There's probably some way around this, not too sure what it is.
I dont know of a way around it. As far as I understand cocoa key processing (and I am no expert) those shortcuts are intercepted by the OS before reaching the application.
One way around this is to set up an app-specific keybinding in Preferences, which can override the default keybinding. I've moved the Hide kitty option to hyper+h, which lets me use command+h freely in kitty.conf:

Some other potential options: https://apple.stackexchange.com/questions/101754/os-x-disable-cmd-h-or-hide-app-command
iTerm manages to do it if you specify a custom key binding, which is why I said there's probably a way.
Well, I am happy to learn from iTerm if you can figure out what it does.
If you figure out how to do it, feel free to send a PR (assuming it requires jumping through only a reasonable number of hoops). In the meantime closing this issue.
It turns out mappings for command+h do work in fullscreen, where the hide option in the menu is disabled. I normally work in fullscreen so that's good enough for me. For non fullscreen mode, manually removing the key equivalent on the hide menu item when command+h is mapped might work.
Hmm too much work at least for me. Patches welcome.
I use this to map "Hide Kitty" to something untypable, and then use Cmd-h in kitty shortcuts:
if ! defaults read net.kovidgoyal.kitty NSUserKeyEquivalents | grep -q "Hide kitty"; then
defaults write net.kovidgoyal.kitty NSUserKeyEquivalents -dict-add "Hide kitty" '~^$\\U00a7'
fi
I find having it as a shell command I can run in my dotfiles makes it easy enough that a hack in kitty wouldn't be necessary.
Most helpful comment
One way around this is to set up an app-specific keybinding in Preferences, which can override the default keybinding. I've moved the
Hide kittyoption tohyper+h, which lets me usecommand+hfreely inkitty.conf:Some other potential options: https://apple.stackexchange.com/questions/101754/os-x-disable-cmd-h-or-hide-app-command