Q: “Why did Legolas and Gimli elude to the fact that Aragorn may have become a terrible lord had he gotten the ring in the Return of the King? Because isn’t he still just a mortal man?”
A: Being immortal or mortal is a detail of little value in itself to decide the power of individuals. Aragorn was more powerful than most Elves; that doesn’t mean much.”
Of course, being immortal or indefinitely long-lived is essential to achieving experience and memory, and if wise of enough wisdom, But in terms of power, not much, for the Tolkien universe follows a reverse scaling; everything is more powerful in the past.
In Aragorn’s case, he was not just a physically powerful Man; he also had great strength of will (and possibly of character as well).
The weakness of the one Ring, besides the possibility of its destruction (but that would have the same effect on Sauron), was that if someone was heroic and powerful enough, that person could challenge Sauron. Of course, challenging the Dark Lord doesn’t necessarily mean fighting the Dark Lord personally using the ring, which even the High Elves could not do. Gandalf could, but the outcome would still be uncertain.
However, the Ring conferred power over minds — the chief reason for its making. If someone used the Ring for this purpose, and Aragorn was strong enough in body and mind to do so, he could I) Build arms and engines of war and possibly II) Control Sauron’s servants and works and use them to usurp his place or even throw him down.
This would be the strategy of the High Elves, the same one Sauron adopted himself.
In any case, Elrond or Galadriel would have proceeded in the policy now adopted by Sauron: they would have built up an empire with great and subservient generals and armies and engines of war until they could challenge Sauron and destroy him by force.
Using the ring for this purpose required more than power; it also needed charisma and oratory skills, the art of influencing people, and the Ring empowered any natural skill to the point where it became magic.
Aragorn was already a commanding figure, so Legolas and Gimli figured he would be a terrible Dark Lord. He was able to command the Army of the Dead without the One Ring, with the power of his figure and the help of the Oath.
In the uplands of Lamedon, they overtook our horses and swept around us. They would have passed us by if Aragorn had not forbidden them. ‘At his command, they fell back. “Even the shades of Men are obedient to his will,” I thought. “They may serve his needs yet!”
That was great willpower, and with the Ring, Aragorn would be an immensely more persuasive and terrifying commanding figure. And if mortality is an issue no more, as the Ring technically guarantees “immortality” in addition to increasing Aragorn’s powers so that he would have become a kind of wraith-lord — exceedingly scary and possibly more terrifying then the Witch King of Angmar, see Frodo near Sammath Naur as a small example than Aragorn would have become.
“Strange indeed,” said Legolas. “In that hour, I looked on Aragorn and thought how great and terrible a Lord he might have become in the strength of his will had he taken the Ring to himself. Not for naught does Mordor fear him. But nobler is his spirit than the understanding of Sauron, for is he not of the children of Lúthien? Never shall that line fail, though the years may lengthen beyond count.”