My tree surgeon pal said they did contract work for the council after storms brought trees down. Back in the day they had queues of folk waiting to uplift logs as they were cutting. This was in Fife on a huge coalfield were every house had a fire. Most council houses have had their open fires replaced with gas central heating, so nowadays he says the council has to take logs back to its depot where they get chipped.
I expect some do, but the majority will be heading out the back door to a firewood processor
I’ve been quite lucky lately as when my tree surgeon pal has a job locally he gives me a call and nip down and clear it away from a neat pile att the roadside. A big change from forest foraging