My guess is there are a lot of potential subscribers reading stories like this and deciding not to bother with a subscription.
Thousands of Americans Waste $348 a Year on Subscriptions They’re Not Using [0]
It makes perfect sense to have a 'shield' that will minimize the 'quitters'. And this article focuses on streaming services only.
People who want to leave a service are probably NOT coming back. So an effort to keep vs lose forever has little downside.
https://www.gobankingrates.com/saving-money/budgeting/americ...
Edit/addition: regarding your ".. I wonder if this isn't a profitable practice though." Well they keep doing it, so.. at some point they ran the numbers and they saw it is better for them. Perhaps in 10y this may change, we will notice by the change of corporate practices. Profit will determine this.
However much annoying these processes are (I had to suffer an identical Financial Times cancellation process last week) They know how much it costs to take cancelling users through an account specialist and presumably they get enough people to continue subscription to make it worth while.
A continuing paying customer now is worth far more than someone who may subscribe again in the future. And even if you're sick of their cancellation process, if you want to read NY Times news again you'll signup.