You can play D&D without thieves too. Try it some time.
I used to think Thief was my favorite character class. It turns out being a Thief guy doesn't rely on Thief skills nearly as much as I thought!
In the old D, with sparse character sheets and minimal reliance on numbers, the Fighting-Man chassis ends up doing a lot of work. A LOT of work. Basically just wearing leather armor and acting like a Thief guu makes you the Thief. Sure you have a way lower chance to do some Thief stuff than a mid or high level Thief guy, but face it: a 1st or 2nd level Thief is not all that much better than some worthless duffer.
Here's a thing I wrote when I was planning the 19th Castle campaign. It's a handout to the player who ants the Thief (or ranger I guess) explaining why he's out of luck at this table, brah.
What, No Thief?
Anyway, the Thief guy is my binky. But playing any of the common races by taking straight fighting man levels and then pretending you took Thief levels instead really works.