One finger playing was common and is not a limitation as long as you can play the line. One finger may be funkier. There have been many one finger or mostly one finger players. Watch Jack Bruce with Cream. Especially common amongst upright players converted to bass guitar.
Tim Comerford talking about Geddy Lee and himself:
'When I'd go see Rush as a kid, I would wonder why Geddy Lee used one finger all the time. Did he do that because it made it easier to play while he was singing? I didn't get it. Later I realized that if you're just riding a note or trying to play a real straight part, it sounds more pulsating if you play with one finger. So I took every bass line and learned how to do it with one finger, and I started doing it that way as much as I could. Back then I thought I looked goofy, but now here I am using one finger whenever I can. One finger is ultimately the funkiest sound of all. If you can do it with one finger, you should. If you can do it with two finger, you should choose over three.'