The ideal way for most "control something" widgets to work is the way the iOS "Apple TV Remote" app already works, when added as a Mission Control button.

It's 1. a regular app; plus 2. a shortcut to get into that app that can be accessed with one swipe from the lock screen; plus 3. a lock-screen widget that displays if the phone fell asleep while the app was in the foreground; and finally, 4. a separate "lock-screen embedded pseudo-app" (sort of like the Camera one you get to by swiping left on the lock screen), which you get to if you tap the "Remote" Mission Control button without first unlocking the phone. This last view allows people to still use your locked phone to pause the Apple TV it's controlling, if you're not there to unlock it for them.

It's too bad that no third-party app on iOS can achieve this same level of integration.

Ideally there would just be a button that could turn on the lights in the room (to the level I want). In olden times this button was mounted to the walls of said room, but in these modern times, it would be awesome if that button was a real button, on my phone, like the volume up/down buttons, and would just turn the lights on/off in the room the phone is in. That Apple's got this hacky solution thats suffciently functional shouldn't be taken as the end-state on what an ideal solution is.

I wouldn't say that's ideal because it's predicated on seeing & using the lockscreen, which is itself not ideal.

Ideal is the device is instantly unlocked when I pick it up - which is also the reality I have as an Android user, but you can experience this on iOS as well with jailbreak mods. And with widgets it's then zero swipes to get to my lightbulb controls, which is just sweet.

I wouldn't see much point in your 3 and 4 for home automation stuff. Homekit does 1 and 2, and for the bulbs I use it with, that's plenty.