OP YABU - unfortunately there are more cars than the space available can cope with, you should expect to pay.
BUT - people without dedicated private parking spaces or residents' parking who expect other people not to park there, YABU too (yes, I know you didn't ask my opinion! ) - you don't have a greater right to park in the street than anyone else. Not even morally. If it's that important, you need to live somewhere with dedicated parking - in other words, you should expect to pay too.
I used to live in the city centre, I had a car because travelling was part of my job (as opposed to commuting), and I almost never could park anywhere near my flat, anytime of day or night. Think a 15-minute walk. But I didn't blame the people who were parked there, commuters or residents.
The only people I think are really hard done by are the people who have driveways which get obstructed. That is really not on. I would call the police or the anti social behaviour people. I was gobsmacked at the audacity of the man who parked in someone else's driveway! My parents have a driveway, and they don't even like people using it to turn - so they keep the gate shut. It's a pest but that's what they have to do.
As for the rest of it - well, after DCs came along we live somewhere else, no car. Much easier anyway to shop by pram, children always appropriately dressed for weather (which is hard to achieve if you are taking them by car), under restraint and everyone and everything kept together till you get to the front door. OK you can't do a weekly supermarket shop like that, but it was fine for our purposes. Now they are older I have a bike and trailer, and it's the same. I don't need to rely on the selflessness of car-drivers ( as if) to get to my front door.
We are about 2 miles from the town centre (nursery and school are in that direction too; so is my work now - different job - pays less but chosen for location as much as anything else). There is no bus service for getting around town, but we can get a bus (about a mile away from the house) to go further afield. We hire a car once in a blue moon. Believe me, it makes you think very carefully about what you "need" to do.
So - in my view if you absolutely need to rely on a car, you should live somewhere that accommodates that need. Personally I have found doing without is brilliant.