TPS and FPS offer different enough benefits to the point where I feel it's not right to say one or the other would flop because of past game design.
Third person is better overall for puzzle design because it is easier for players to look at the larger picture. It is also better in terms of animation design and combat as the player can actually use noticably different fighting styles.
First person is better for certain narrative elements such as horror games or to make the player feel like the main character. It also provides benefits with shooting as aiming can be more accurate (though some TPS go to first person when aiming, mostly with snipers). It also makes the game more picturesque.
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I personally prefer 3rd-person when combat is melee-centric, or, roughly half in the case of Warframe. When shooting is the main focus, I need 1st-person. I'm dying for a Destiny-style game but in the Star Wars universe. Unfortunately, I don't see that happening.