Objectives Shouldn't Give Gold
Objectives giving gold is one of the big reasons why games snowball out of control. Assuming your team takes an objective first, you already gain a large advantage: the ability to roam, easier farm, dragon buff, baron, etc. These advantages are ones that change the flow of the game, not just speed of acquiring items. Teams get enough of an advantage without the added gold, which just makes comebacks harder.
First tower team has had a ~70% win rate for ages because of how that team is able to change their strategy after the tower is down. They don't need gold too, it just reduces the chance of pushing back. Not just for first tower, but all towers, dragon, and baron.