Getting a flat tire is never fun, but all flats are not created equal. My black bike has had a slow leak for months. I have to pump it up every few days. Surely I’ve spent more time and effort inflating the tire by now than would have been required to patch the hole or replace the tube. This is my least favorite kind of flat. It’s a long term drain that’s never quite inconvenient enough to demand fixing. Sometimes they linger until a second puncture forces you to remove the tire anyway.
In contrast, when you run over a big piece of glass as you’re rushing home with drinks for people who are supposed to be showing up any minute, there’s no ambiguity — you just sit down and patch it, right there, right then. If it’s obvious where the hole is, you don’t even have to take the wheel off the bike, and it turns out not to be such a pain in the butt after all.
(Especially if you remember to unseat the bead of the tire all the way around before trying to lever it off the rim… D’oh!)