I thought about this, and man, I think people can just limit themselves if they want. A fun arcade game is fun on its own. Taking away infinite credits isn't going to magically fix the design elements centered around the game. FF games are still going to have cheap bosses with dumb hitboxes and too many i-frames while you get stuck getting smacked out of combos.
On the flipside, The Simpsons was fun to me because of the characters and setting, not the gameplay. No amount of holding back coins was ever going to make that fun.
I disagree about infinite credits being a better default, if that's what you're saying.
Challenge is what makes a game, for me. Assuming the game is decently designed, the fun is in facing a challenge and learning in order to overcome obstacles. If you can just breeze through it, you may have an acceptable experience, but it won't be very meaningful.
I remember, before having this kind of discussion, loving that Metal Slug 3 was on PC.. After jumping into the game with a friend, it was a blast for a level or two, but once it set in that we had infinite continues, the mood changed and we were just going through the motions.
Looking back, some if my favorite, most memorable game experiences were very challenging. Many of my favorite games I've never really beaten.
Concerning arcade games, sure, your credits are only as limited as your wallet, but when I was a kid playing arcade games, with maybe 5 dollars or so, I was only willing to drop maybe 4 quarters on a single machine.. If I was really close to winning, maybe I'd muster up another one or two quarters, but there's definitely a sense of limited lives, and every life feels precious and worth fighting for.
Not that arcade games are particularly well designed, but that's often why having the inherent challenge of limited credits adds something to these games.
Edit: I'd also like to add that it's easier to go along with the rules the game presents. You could ask players to make their own rules and limit themselves if they want, but it's hard to say what our limits should be. It's always best if a game is designed with challenge already prepared. That's why difficulty modes exist. So players can quickly jump into an experience most suitable for them.
I'm tired and rambling, but I hope I've gotten some of my thought across. Challenge is very important to me..