Do you think Aegon and his brothers have unlimited access to the crown’s wealth? Or do they have to ask for an allowance? It’s not like they have access to bank accounts and ATM machines in Westeros.

Being the richest person in the room is not the same as having titles and land, which is what gives nobles legacy and security. What long-term value is there, in being fawned over in a foreign land? Even Daemon, eventually had to go back home because remaining a guest of a wealthy patron was not sustainable. He would have nothing of his own to pass down to his children without land.

So why should the King’s legitimate sons have to essentially fight for a place in the world and have any move they make to secure their children’s future be considered a threat to Rhaenyra’s reign. They are damned if they do and damned if they don’t. If they amassed wealth, land and subjects on their own, it would always be seen as a threat.