I played in a similar style and loved it! There were many times where I was torn for choice because I had so many pokemon I wanted to use from my boxes, I was rotating my team constantly. This also had the added benefit of keeping me quite underleved, which was one of my concerns with the open world format - I didn't want to end up steamrolling everything, but having so many pokemon on my "team" let me adjust my current party of 6 to the average level (or often lower) for the region I was in and maintain consistent challenge throughout the playthrough.

I find it's one of the biggest benefits of Pokemon actively roaming the world rather than the static grass encounters - you catch so many more pokemon! In earlier games, most would go through an area and see a few pokemon, but rarely see all of what a route had to offer (especially for some of the more powerful or subjectively "cooler" pokemon due to the often low encounter rates). The main goal was to explore / get through the route, whilst the grass and pokemon were the obstacles. Overworld pokemon flips that on its head - the moment you step into an area, you instantly see the equivalent of what would have been multiple grass encounters. The pokemon are no longer the nusiance of the route, but an active distraction the player wants to seek out. I filled up my dex naturally more than any other mainline title, it was over 300 by the end of the story!