Increasing the FOV can potentially cause performance issues, but it depends on the game. In my experience (on a base Xbox One) some games, like Doom 2016 and RDR2, can handle a wider FOV with no frame rate problems. Battlefield 1 was a different story, I did see some occasional frame rate drops, but they were infrequent enough to not disrupt the game.
All that being said, the Halo games in the MCC should
be able to handle a wider FOV on the current gen of consoles. Halo: CE already has an approximate FOV of 86° and Halo 3: ODST is at around 88°. The real problem here is Halo 3, which only has a FOV of 70°, giving it more of a tunnel vision feel.
. There's a breakdown on the approximate FOV of all the Halo games up until Reach.