I can see if people had a problem with there being 'God' Slaying magic, since there's yet to be any mention of gods and all the characters using it appears to have learned it from books.
However, Devil-slaying magic seems obviously more practical, useful, and likely for humans to learn. Namely since there've been countless demons introduced during the series (Mira's takeover, the island of demons, Deloria and Lullaby, other demons from the book of Zeref, Hades creating demon from rubble, etc.)
Dragon Slayer is the only one introduced where they learned from the actual thing they're slaying, but I don't have a problem with there being multiple forms of slayer magic - provided it's something practical that a human would need to use against an actual opponent.
Just like there are multiple types of guilds (treasure hunters, merchants, mercenary, bandits, etc.) outside of the main one (mage), there are multiple forms of slayer magic outside of the one initially introduced.
It expands the FT universe to introduce new magic types, and new guild types. Allows new types of characters and interactions.