It's less age of sail and more the age of medieval knights if you are looking for a comparison.
In medieval times, knights would claim the equipment (and horses) of captured or killed opponents. This was not just lucrative; it was often vital to the profession. An individual knight was largely responsible for outfitting themselves. Armor, weapons, horses, all of this was expensive. Plus, actual currency pay for an army could be very inconsistent.
Even some of the tournament-like events (which sometimes got pretty lethal) would see knights get the opportunity to claim stuff. Very successful knights might walk away with a number of horses, weapons and armor.
I'm not aware of any specific examples in Battletech of prize money for kills. But there are some nation military rewards/awards out there that come with land grants and titles (or giving them ownership of their 'mech). I could definitely see some mechwarriors earning some of that stuff for basically lots of kills, though the citation might read something more like valor in combat and having an outsized contribution to winning a battle.