I feel your pain. I’ve had the same issue — especially when trying to log into streaming apps or typing passwords. I actually gave Eltima’s TV Remote App a shot a few months ago, and while I wouldn’t say it’s revolutionary, their on-screen keyboard is a solid step up. It pops up automatically when a text field is active on your TV (assuming you’re on the same Wi-Fi and everything's synced properly), and it syncs decently fast. You can even use your iPhone’s native keyboard, which for me was way more comfortable than poking around a TV UI with arrows. I’ve used it mostly with my Android TV box, and while there are occasional hiccups in detection, it’s better than what I got with a few free apps I tried before.
You can check out more about it here if you haven’t already:
Roku remote app for iPhoneHonestly, I think this kind of feature should be a standard. There’s still a bit of lag sometimes (especially on older smart TVs), but it’s definitely usable. Would love to hear if anyone’s had a different experience though, especially on Roku since I don’t have one to test with.