Yes, like others ours is the 'formal dining room' room, but we prefer a table in the kitchen to make that a kitchen-diner, so it's our playroom.
Totally agree that when they're small they just want to be with you, but I really liked having a totally kid-friendly toy room where I could go and play with them. I guess it depends what kind of people you are - if there's a tv, we'll probably end up putting it on, and then it gets watched / distracting during playing. So I found it nice to have a room where there was no screen, and I could 'lean in' to playing more. We used the Alexa in there a lot to play music (either loudly or in the background) while playing.
Now mine are older (all primary school, but at the top and bottom ends, plus middle), we have put a tv in there, along with a big sofa (charity shop though, so not expensive). It gets used when the kids want to watch different things, and works nicely.
Also, we've put desks along one wall for all three of them, which has worked out well. They like to use them for colouring / crafting, etc. and the older ones like doing that while I'm on the floor playing with the youngest.
Agree with others, also, about shutting the toys away somewhere. My middle child, in particular, is a massive fan of 'setting up' things - one week there's a big Sylvanian street with all the accessories and animals out, and it stretches across the room and she plays with it everyday and it can't be moved; and then the next week it's Lego central, or Barbie city, or towers / zoos using blocks and animals. They'd never get to make those (and then keep them out for a week) in the living room.
Gradually it will become a more tween den and be like a second living room that has desks and board games. But not for a few more years.