Perhaps, but that's as much Gandalf pulling the strings and pointing the dwarves at a hobbit worthy for other qualities than actually being a competent burglar. They still hired one one to fill a needed role - that of the traditional thief in AD&D.
I'm not saying LOTR didn't have an influence on the game. It had a large one. But not on the way the game played so much, because, well, take Bilbo for example. I think you're right, Gandalf did choose Bilbo because he was exactly what was needed for the mission. But not because he was a good thief (in the D&D sense), but because he was far more crafty, wise, and moral than even many of the people around him. He kept the dwarves honest, dissuaded the continuation of the war, tried to be fair to everyone, and tried his best to get everyone to share the wealth of the horde, not fight over it. He was in short the most moral man in the entire book, short of Gandalf (more of an observer in the Hobbit), and I think this is what Gandalf wanted and expected of Bilbo, at least in part. Not just a clever burglar and adventurer and explorer, but a real moral influence. Bilbo was not the typical fantasy thief idea. In that I think we likely agree.
Now early on I remember many people, myself included, trying to play the
"moral thief" as taken from Tolkien. Take (or retake actually) only from the evil, try to be fair to your own party members, try and do what is best for everyone if possible. The opposite of this ideal of the "moral and honorable thief," or what could really be called the rogue with the good heart in another respect (to use a modern example,
Burn Notice - I personally have always liked the rogue who appears as one thing but is in truth another, because in truth he is really a sort of undercover Dick playing a bad man, but twisting things in another direction), is the assassin. But eventually I noticed that the thief, for the most part, and for most players I associated with, became more and more, over time, the Conan type, or even the minor assassin-like character. A cunning, back-stabbing, footpadding, guile-filled manipulator and schemer, even against this own party.
I personally am sorry that happened, that the moral thief ideal died out and left only the amoral and immoral ones. But that's the way the game developed for the most part.
But I'm not saying the game was uninfluenced by Tolkien, it was heavily. But over time it became far less so, especially regarding the moral basis of certain characters that might be loosely considered Tolkienish. Though Bilbo was never the typical fantasy ideal of the thief in the first place. That was my point. In many ways he was the obverse, or even the anti-Thief thief. I think Tolikien did that on purpose just as he made Gandalf both a prototypical Middle Earth Wizard, and something very different from the prototypical fantasy Wizard in many other respects.
Characters (and in the case of AD&D the PHB) was heavily influenced
The Game Play (and in the case of AD&D the DMG) was not so much.
I think those are good, general points.