I'm not really sure about the crystals.... I didn't see him pick up any loot from the monster from his gate.
This is my opinion.
By killing the monsters, MC gets to level up his weapons and get stronger, but for him to get strong monsters, he still has to get the crystals from the tower and feed them to Burnheart. So basically, the monsters that come out of the gates that Burnheart can open help MC train. And to increase the difficulty level of those monsters, he needs to feed the gate crystals from the tower.
It would be too convenient if the monsters from Burnheart's gate dropped crystals. And in theory, the gate's level would not rise if that were the case because the number of crystals in the gate would never increase, making the gate's growth stagnant. (=・ω・=)
Ok, so correct me if I'm wrong but Brunheart can open a gate with monsters and those monsters can drop items and crystals. He can also feed those crystals to Brunheart and continually level it up improving the gate ability which I'm assuming also improves the quality of the monsters thus improving the drops as well. So he's basically has no need to go into the tower no? He has everything he needs with that gate ability I would think.