Based on the single stream comment, I'm going to assume you're describing an experience in North America, and your assumptions are pretty off base for PET bottles.

Figure 1 in the linked paper gives the raw numbers for where PET bottles end up. [1]

[1] https://onlinelibrary.wiley.com/doi/10.1111/jiec.13496

Yep, I've worked in recycling for 6 years and am well aware that there's a lot of broken parts. My point was that if a PET bottle goes into a single stream system, the recycling industry is pretty good at capturing it, baling it, and selling it to a plastics processor. That processor will clean it, pellet it, and sell it as rPET. 85% of PET bottles that end up in curbside single stream end up getting recycled. I'd like that number higher, but it's where things are at the moment. Throw a bottle in the trash, it's getting landfilled/burned. Throw it in recycling, it's most likely getting recycled.

In Australia the whole hard VS soft plastic blew up recently. The REDcycle brand by mayor supermarkets was shown to just collect and store the soft plastic in large warehouses. For bottles there is a refund scheme.

I worked in an office with recycling bins where everything was just gathered up and thrown in the dumpster with the rest of the garbage. It wasn't just our cleaning people, either: from my desk I could see the only two parking lot entrances and while the garbage truck came weekly, never once did I see a recycling truck.

PepsiCo did the same thing. Custodians dumped everything into the same bags. Leadership confirmed it all went to the dump. Still had a personal recycle bin crammed under every desk.

This is just corporate virtue signaling.

And/or ass-covering. There might be contracts in place etc.

More likely it costs the building cleaners time & money. No economic benefit for them so they don't bother even if overall there might be a benefit. Incentives need to align.

My town uses the same trucks for both.

likewise at a large office building I'm familiar with

it was said that because employees/building tenants contaminate the recycling bins with unrecyclable items including food waste, there was no point to do anything but combine it into the trash

however the recycling bins were kept presumably to keep people from protesting about trashing everything, and the memory of this news quickly faded

the same goes for recycling bins in downtown toronto - they're so contaminated that they go straight to landfill

You might not be seeing what you think you're seeing, WRT everything going into the same truck. Lots of municipalities (e.g. mine) undertake resource extraction from commingled waste & recycling streams. It isn't the same everywhere, but sometimes it's more efficient to just put the entire waste stream through the same extraction process to recover recyclable materials. The separate receptacles at the client side are obviously redundant, but sometimes those remain from legacy processing arrangements.

I heard this as well. There is a recycling plant that you need to run anyway to separate the waste/rubbish so you might as well use it to get the plastics and cans out. I think there is an argument that while the machine can do it well avoiding the machine does have benefits. This also doesn't work for paper or cardboard as it would get soiled from what I understand.

The real benefit of separate sources is those machines cannot handle things like plastic bags (they get caught in rollers and jam the machine), dirty diapers, and other such weird stuff. Once you get those out of the stream you may as well separate a few other things that are not recyclable so you need less of the expensive separation machines. However you always need sorting machines - people will make mistakes and so you need to verify everything really is recyclable.