I feel like people really often do things just because they've already started doing it.
One example could be the Electronic Evidence of Sales just established in Czechia. It's a system monitoring all the sales in the country by receiving electronic bills. Now, in order to launch it, every shop in the country had to buy a special cash register so we already invested a lot in it but some say it's ineffective so we should cancel it. And, of course, everyone says that would be dumb once we're using it but they don't realise that our past decisions are irrelevant for what we choose now, that is, a system with less effectivity. Note this story is just an example of a bad argument and might not be true.
The closest phenomenon I could find is the naturalistic fallacy and appeal to tradition fallacy. Among friends, I call it "the finishing syndrome", isn't there a more widely used term?