The only time this was ever a problem for me was when I tried to use a Gameshark and wanted to put codes into a saved game. The Gameshark card has to go into slot 1, and the ps2 couldn't detect my saved game, or even the memory card itself, in slot 2. I rarely ever use the Gameshark anyway, usually just if I'm giving a game a second playthrough and want to sprint through it invincible or something, so it hasn't been too big of a pain.
I've got two PS2 memory cards, and it took me forever to fill the first one. I've probably had saves for around 40-50 games at one time or another, so I have had to occasionally just delete saves I don't care about anymore. Not a big deal.