The issue with this is WoW already had the basis for critter finding in game, they had little critters that ended up being used as pets later on. XIV has no such thing beyond the minions. There are a lot of minions in the game but a lot of them are absurdly hard to get, it's not a bad idea but it would be a lot more work on trying to collect them, WoW also has multiple of the same pet allowed in different rarities, XIV doesn't have anything to that nature. Then there's the rarity issue and balance, would people like it if say Alexander or some very rare minion wasn't more powerful than the average minion you can buy off the mb for a handful of gil? People already complain massively about job balance I could only imagine the storm of complaints about this minion being too powerful or that minion, then you have people abusing the system. Lastly if no reward it's unlikely for anyone to want to do it other than people that really love that sort of thing.