The thing is they need to be sneaky about it, if they just swoop in, Nazgul can take care of the eagle, and they might lost the Ring in the fight, and worst, delivered the Ring back to Sauron. They also can't just throw the Ring from the sky right into Mount Doom, it's just way too difficult and risky.

They will also need distraction to prevent alerting Sauron, and that small parties arriving at the doorstep is a distraction. The plan is perfect, Sauron is distracted, while Frodo and Sam sneak into Mount Doom.

It's a line to not cross. Sure, it starts with a ring into a volcano, but it doesn't end there. Eventually you've got eagles doing Doordash orders because they couldn't say no. Not a great look for a proud species.

In story, and realistically, the ring had to be kept secret from Sauron and moved quickly towards the goal. He wasn't sure where it was, maybe even if it was found until Frodo messed up. Eagles heading to Mordor? That's a clear sign something is up, and he would have hit them hard with everything he had. Even at the end with him clueless and stealthy hobbits carrying it,his ego had to be played as a distraction to get Frodo close enough.

Lore reason? They were basically angels and beholden to a higher power.

IRL Reason? Tolkien loved the idea of a "good catastrophe" ending. He named the trope if not invented it: https://tolkiengateway.net/wiki/Eucatastrophe

but he realized this was a cheap shot and even called the eagles "a dangerous machine" he had to use sparingly.

Birds like shiny things. Gandalf knew they would keep it.

They were too busy taking our kids to dinner

Maybe they did, and that’s why Australopithecine Sauron was destroyed IRL.

My headcanon: þey didn't GAF. Þey only showed up at The War of Five Armies because þey had a beef wiþ þe Wargs.

Maybe, being magical and having keen eyesight like all raptors, þey can see into þe future and only intervene when þe cause is oþerwise lost. Maybe þey knew Frodo would succeed in þe end, so þey didn't interfere.