I actually played in a rock band (I should add a LOUD rock band) where we decided to forgo amps. Bass, drums, keys/sax, guitar. Not one amp. I ran the keys/sax, guitar, and a tiny bit of bass through the monitors (12"), and of course the vocals. It was relatively quiet onstage, compared to previous. It lasted about four months, after the guitarist decided that he couldn't hear himself well enough...and then the keyboardist couldn't hear himself over the guitarist's amp, and eventually I had to get back into the loop with an amp. It was fun - and quiet - while it lasted.
I have shown up at an outdoor festival where a backline is provided, only to find that they didn't provide a bass amp. I just ran into a DI and let the guy out front handle it. Friends told me that they didn't notice a difference in the sound, but we did onstage.
No, you don't NEED an amp, but they are nice to have as monitors. My current gig-rig is a Shuttle6.0 and Bergie 1x12. I can hear it just fine.