Hmm, Rivalry might make Haxorus a bit overpowered (complete counter to Dragonite/Salamence/Garchomp).
Analytic might make Starmie a bit overpowered (immunity to Thunderbolt)...
Pretty sad, since they're pretty nice thematically.
Telepathy has excellent distribution, as do Frisk and Forewarn (nothing in OU get these). Out of those, which do you think should get these, Katakiri? We could also apply it to multiple of these.
Telepathy wins easily out of those three. There's a bit of overlap with Musharna since it has both Forewarn and Telepathy but the biggest reason I'd like Telepathy over Forewarn is that Musharna does most of what Hypno could do and Gardevoir eclipses Jynx due to better typing.
With that said though, Gardevoir, Musharna, & Beheeyem need a new move or two that take advantage of their ability, much like how Game Freak gave Spinda Superpower for Contrary. (Wobbuffet and Medicham would never give up Shadow Tag and Pure Pure Power, so they're fine) That's also why I don't think Frisk should get the mechanic simply because we'd have to give new moves to too many Pokemon since they're in the same boat as the Telepathy users. (Minus Yanmega & Gothitelle, who would rather keep Speed Boost/Tinted Lenses & Shadow Tag.)
I have thought this out a little so here's a couple suggestions:
Beheeyem: U-Turn
This gives BEM a small niche as a Trick Room setter. It comes in on everyone favorite move, throws out a Trick Room then can either U-Turn out itself or go on the offensive with it's high Special Attack. U-Turn (とんぼがえり Round-trip) also fits with it's visitor motif as well as it's ability to levitate.
Gardevoir: Sketch?
Every fiber of my being wants to say Sketch via event. (Probably because she has Trace and it matches.) It would fit her ability perfectly by letting her block one specific move to be tailored for taking on a specific Pokemon. My only concern with Sketch is that she gains access to Quiver Dance and Shell Smash. This would let Trace Gardevoir come in on Heatran's Fire Blast, Thundurus-T's Volt Switch, Jellicent's Scald, or something and just set up for free. She's got all the Defense of a wet paper bag and base 80 speed is nothing to write home about even after a QD so offense & mixed shouldn't be too threatened, but Gardevoir could tear apart stall teams if given the chance since she has Psyshock and an instant +2/+2 boosting move available.
Musharna: Scald, Fire Blast, Flamethrower, Will-O-Wisp
All of these moves go back to what Musharna is based off of (aside from a Baku): traditional Japanese incense burners that are commonly shaped like pigs. Scald also combines that with it's sleeping theme by being heated mid-sleep drool. Competitively the Fire moves do wonders for it, but don't do a whole lot for it's ability. I drew a blank on what exactly it could get to use Telepathy with but in the process I found a few moves it thematically should have had in the first place. Musharna does stop opposing Calm Minders like Latias so it might have it's uses even without a new move.
But yeah that's all I came up with so far. So much theorymon.
Edit: Actually, since it's Event-only, Trace Gardevoir wouldn't even have access to Sketch and Encore's an Egg Move so she wouldn't have the chance to set up QD or SSmash aside from coming in on a Gengar while she's carrying Shadow Ball or landing a Hypnosis (and wasting a coverage slot for it as well.) It's still a little scary for stall but Sketch Gardevoir is MUCH more tame than I thought.