I have never liked the "20 = critical success = always succeeds", mainly because I can with a 5% chance end a "Destroy Sauron's ring" adventure in 40 seconds with "I attempt to destroy it by hitting it with a hammer, like, really hard."
Rather than "destroy sauron's ring", it's more like "you dislodge a mysterious gold coin that was stuck to the bottom of the table".
For example, if the player is attempting something totally stupid the 20 result might even be "and nothing bad happened", as nothing better was possible (for instance it is impossible to break the one ring with a hammer, so even not totally wrecking your powerful hammer could be a great outcome of such a foolish action).
Or a 20 for asking the eagles for help might be that they bring you half-way, as the eagles wouldn't want to get too close to Mt. Doom anyway.
I'd also add that ideally (if the DM is fully in the spirit of how this can be played for maximum creative storytelling potential), asking/negotiating for the assistance of the Eagles wouldn't be a single quick dice roll, but rather a complex, possibly hour-long session of courtly intrigue, diplomacy, and politicking, featuring many dice rolls, a lot of carefully chosen words, and a lot of favor-trading and maybe even intimidation. Ideally, getting straight to Mt. Doom via the Eagles should really be achievable, but not with just a single roll of a 20 - rather I imagine it would perhaps involve a concerted and creative effort by the whole party during at least an hour of playing time.
And then, there will be numerous dice checks to survive Mordor's anti-air assets (including probably cool eye beam lasers from the Eye of Sauron tower) and to accurately land the ring in the volcano despite buffeting wind. If any of those checks fail and the ring falls into inert dirt, the party would probably have to quickly send a commando team into Mordor to rapidly finish delivering the payload to target before Sauron's mages arrive in overwhelming force. Would honestly be more fun to play through one of these semi-failure disaster scenarios than an easy win!
Even if / when the party defeats Sauron, they don't have to stop there. For example, they could set their sights on investigating and stopping the reason for the waning of magic from the world, or any (ideally noble, or at least villainously entertaining) goal of their choosing. They could even e.g. research and create dimensional travel magic and hop to a totally different setting such as that of Star Wars.
If they complained that they didn't get a chance to roll the dice, I'd explain to them that they're misunderstanding the purpose of dice in the game - it's to provide randomness to situations where outcomes are uncertain.
In the inverse case, I wouldn't make someone roll the dice for mounting their horse when breaking camp if their character is someone who is familiar with riding horses, or to not spill their flagon of water when taking a rest in the dungeon.
Particularly for older versions of D&D, players went out of their way to avoid rolling dice whenever possible - dice are dangerous! Roll poorly, and you don't succeed. You might even die! And the ability to resurrect the dead is far more limited for older editions - player characters being effectively immortal outside of TPKs is a much more modern change.
“Success” on a roll to hit with a weapon is just that: hitting, not destroying. And, well, hitting the One Ring with a weapon doesn't short-circuit the adventure (see Gimli at Rivendell.)