If trying to rationalize things - I'd say Sauron knows that giant eagles are a thing, and able to serve as mounts. So to prevent Western aerial reconnaissance and insertion/extraction of observers/spies/special forces in Mordor, he's got to have some sort of aerial observer / aerial denial systems going. Which systems would make a "fly the Ring to the fire" gambit too risky.
(Vs. voice-of-canon Gandalf makes it clear that anyone seeking to destroy his Preciousss is simply beyond Sauron's Vile McEvil worldview.)
Exactly.
In fact, when Gandalf catches up with Aragorn/Legolas/Gimli in 'The White Rider' chapter, he explicitly tells them that Sauron has committed a major strategic blunder: attacking too early, as soon as he thought the Ring was in play. If he'd kept some forces back to guard Mt Doom, he'd have been alright. Especially because, as later becomes clear, Mt Doom isn't a normal volcano where you could just lob the Ring in from your low-flying eagle. The Cracks of Doom are in a chamber deep inside the mountain.