Glass, aluminum, and cardboard are almost always profitable to recycle if the city is big enough to make it worth the infrastructure expense. It's the recycling of plastics that we were scammed into thinking made a difference. It does not. Twas a clever move on the part of plastics producers. Meanwhile most gets either a. dumped in a local landfill (after added expense and hassle of collection and sorting), b. shipped partway across the world and dumped at sea, or c. shipped all the way across the world and burned. Note, there are two specific types of plastic that can actually be profitable to recycle, Numbers 1 and 2 (PET and HDPE). The rest is pure junk.

Compost may be similarly beneficial, depending on public compliance, the market/public need for the compost product, and how efficient a particular region can make their system. It is certainly not a one-size-fits-all kind of deal, and probably is not even worth attempting in some regions.

The headline says 'plastic recycling' whereas the GP's claim was about recycling and yard waste in general.

What about yard waste?

Your original claim was 'almost all' so if you're just talking about plastic I think I'm quite right to question what you 'heard from the garbage guy'.