The reality was that "quite far away" wasn't consistent and depended heavily on your environment. I've used the Wii U a few times in recent years, and its range and reliability has noticeably shrunk compared to when it was current - presumably due to the rise of 5 GHz Wi-Fi networks (that have only gotten more powerful and higher throughput) interfering. Even when it was current, the Wii U at my friend's place in a higher income neighborhood with more spaced out houses had much better range than mine. And I know some had it worse than me; it was especially rough in apartments, which tend to cluster a bunch of networks in a small space.
Nowadays I'm lucky if I can get through an hour session with my console in direct line of sight of the controller less than 10 feet away without the connection dropping at some point. It was never like that before, but it is now - and it's the same with my other friends that own Wii Us.
I can't personally speak to Remote Play. Maybe it has gotten better, maybe your environment wasn't ideal to start, who knows. But I feel that direct wireless has become less viable in the last decade, not more. Even if you went with something like 6 GHz, that has less range to start - and it'll just hit the same problems as Wi-Fi 6E becomes more widely adopted.
I'm curious - when you say wired, is that end to end? PS wired, phone wireless? Going through the Internet at all?