As stated by many, the quests are made THEN voice actors are hired. So the amount of voiced parts does not translate to fewer quests.
But if your game was a mix of major and minor characters ~majors having voices (as Fallout did), then even after the studio sessions are long since finished, you are still free to add what you like to the game; using non speaking characters to introduce your quests. Fallout 1 & 2 had this built deliberately into the design. Where NPC heads (like Loxely and the advlt Tandi) would speak to the PC at length about the major issues, but also had set aside a recorded dialog that said, loosely "Speak with my assistant about that, he ( or she) will fill you in on the details". This allowed the developers to tack on any content they liked as a quest from a major NPC, and not have to have them actually speak about it. Their assistant NPC (like Jasmine, in Loxely's case) would handle the instructions and rewards.
Had this been done in Fallout 3, user quests would not require NPC voice tracks to seem normal.