Is there any good reason to make a skill legendary? [duplicate]

The main reason to Legendary a skill tree is, as you said, to allow the player to level indefinitely. Originally, you could only level up until all your skills were maxed, and then you would stop leveling up. This restricted players from reaching the levels necessary to unlock certain late-game spells, so the devs changed it to remove the level cap rather than lowering the levels required for those spells. In doing this, the devs also essentially made it possible to endlessly expand your magicka, health, and stamina limits (and therefore, with the latter, your carrying capacity). I have seen players devote so much time and energy to a single save game, that they can sprint the whole way from Solitude to Riften, casting Flames nonstop the entire trip. Now, many players rely only on a few skill trees in a playthrough. For example, most of the time, I never use heavy armour or smithing. In the old system, this would have meant I was level capped even earlier than other players might have, unless I decided to start working on those skill trees, which I would rarely even consider doing. In the new system, I can completely abandon and ignore any skill trees that I do not wish to use in a save game, and still level endlessly.

Now, you specifically asked if there was any other reason to Legendary a skill. And the answer is: Yes!! There are now real perks to Legendarying a skill tree. When you make a skill Legendary, you unlock a permanent bonus to actions that rely on that skill tree, as well as an XP boost from those actions. Some mods and CC addons add other useful things to the Legendary option, but the base game and DLCs only have those two perks.