I've always personally found the Lake Guardians to be kind of bland, so if GF had made the trio all part fairy at the outset of when they were introducing the new typing, I would've been completely down with that. Now, however, I'd probably resist it for a battle and pokemon development reasons.
Looking at the spread of Fairy pokemon, I think there are only seven different kinds of fairy dual-types. That being said, adding the trio now, either as pure fairy or fairy-psychic, with their current various statbuilds and movepools would be kind of a shame in the long run.
One of the most exciting things about this new typing is to see how GF will fill out the roster in following generations. If the trio are included now as pure fairy, every new defensive fairy will have to compare to Uxie and all new offensive fairies will have to compare to Azelf (fast/frail) or Mesprit (balanced). It's probably for this reason we don't regularly have normal legends (even then, Arceus should be omitted for godliness and Regigigas for suckyness).
From here on out, to stand out, a new fairy would need to have either a) more polar stats than the trio, b) higher base stats than the trio, c) a more useful ability than Levitate, or d) a useful secondary typing. The mono-Fairy type would pretty much peak as soon as such the switch was made.
Making the trio Psychic-Fairy carries the same pitfalls, though possibly to a more extreme extent as now a Fairy would need to ideally carry a secondary typing better than Psychic, a type which is super-effective against one of the type's only two weaknesses
From a name and theme standpoint, it definitely makes sense to make the Lake Trio part or all Fairy, but from a game standpoint, I hope they stay right where they are