My guess is one of three things:

1)To prevent people from blasting through leveling. Beast Tribe quests even from ARR give a lot of exp for below 50. Generally doing your normal three gives out around 35% percent. Having that uncapped would be pretty insane as no one would run dungeons and every time you would try to do your personal beast tribe quests multiple people would be spawning theirs. The red chocobo event for Lighthouse is a really good example that everyone trying to do the exact same thing at the exact same time turns into an absolute mess.

2) To make the exclusive items have more value. The beast tribes themselves have some exclusive items for rising through the ranks. The ARR ones have dyes/housing items/orchestrion/mounts that can only be bought through them. The HW and SB ones also have glamours/orchestrions but also most importantly crafting items. When Stormsap first came out in SB the sales for it were absolutely nuts since it was needed to make the BIS crafted gear at the launch of the patch. If those items were just available to anyone due to no limit cap the value would drop and everyone would be doing it. Why not make the most out of it even if you don't craft?

3)Bots. Leans into 1 but is big enough for it's own issue. If bots were allowed an unlimited amount of Beast Tribe quests, those quests all give exp but also gil. You see how rampant they are in Ampador Keep so much so that dungeon can't be accessed at times due to them. Wouldn't be shocked to see bots take advantage of an infinite pool of free gil with no time restrictions and crash the market even more so then they normally do.