YES, not enough inventory slots!
NO, just dismantle/discard what you don't want
We each get 60 slots total (right?), anyone think that's just not enough? Especially as you progress further into the game getting more exotics?
Well keep the exotics you actually use and dismantle the one's that are just taking up space. Like if i got bad juju as my first exotic (pulse rufle) I would never use it because i hate those and would probably dismantle it next time I got an exotic weapon.