Is it possible to, without any extra knowledge, send a transaction back to whoever sent you monero?
In say, bitcoin, I know the address of whoever sent me btc, so I can send something back to them without them providing us their address "explicitly". Can something similar be done in the monero protocol?
this concept has been discussed before as "return addresses". it would marginally increase the transaction size and thus the storage requirements, but it's possible and seems reasonable. it looks like no one pursued it since knaccc formalized it. nevertheless it's on the roadmap ("Future" tab).
"bloat" would be an exaggeration. if you take 1 in / 2 out transactions as representative, it's a ~2% increase in transaction size (presuming knaccc's numbers apply to the presently used Bulletproofs+ transaction format).