When it comes to plastic recycling, the usefulness varies greatly between countries and even inside countries depending what kind of facilities and other infra there is to utilise the plastic from the bottles.
While a lot of the plastic from the bottles doesn't end up being reused even in the best case scenario (currently, it is being developed forward) I still think it's better to use at least some of it again versus stuffing it all to landfill straight up. Or not gathering it at all and leaving animals to deal with even more waste than they already do.
In some places, the plastic that doesn't come out clean enough to be made into bags and T-shirts, then goes to burning facilities that provide heating for local housing. In other places it gets dumped with horrible consequences. The two polar opposits currently. It can be really hard to know sometimes, exactly where and what happens to your local area recyclables, but it's worth finding out, because it varies so incredibly much.
If I lived back in the forest where I used to, I would not recycle cardboard, because there they don't reuse it, they dump it, in lack of anywhere to take it to be reused or even burned. I used it myself in the garden.
In the city now, close to an insanely good burning facility, I can recycle everything with a good peace of mind. Everything from this area either gets reused or burned and even the burn waste gets used. There's barely any landfill waste from households in this area. Just two cities over they do.