For players who don't read very well, the only option is pure memorization. Their reading is too poor to be of much help in a performance situation, so the piece must be learned by heart in its entirety. This is doable though the number of pieces you learn is limited by the number of pieces you can memorize.
For excellent readers, pieces can be played with little or no practice. "Prima vista" ("first sight") reading is not very common but it does exist and it's an enviable skill which takes years to develop. The number of pieces you can play has no limit since you're not relying on memorizing. Few people attain a level of reading high enough to play all the pieces they want, but it's not impossible.
In between are the rest of us, and it's not a bad place to be. We can't read something accurately at full tempo the first time necessarily, but after say the tenth or twentieth time (or more) we do quite well. We partially memorize the piece, and read well enough that the sum of our memorization and reading skills are enough to play the piece.