My dd just follows me around so toys end up being carried all through the house!

I think if you move the toy boxes out of the lounge room then at least when you clean up, the lounge room should be toy free. My dd has a lot of games set up in different areas of the house, so if I clean up the toys on one space it's not like she can't play iykwim? I also put toys on rotation so she maintains interest...so her craft table gets replenished often (with new toilet rolls lol) which means she doesn't rely on one box of toys.

Not sure I answered your question, but I think it's fine to put boundaries around where toys 'live'... Like indoor/outdoor toys, or kitchen only games etc.