Doesn't FTL also imply time travel - which probably isn't a good thing?

I think wormholes and warp sort of get around it by having the FTL traveler moving slower that light in their pocket/hole through space.

SPOILER ALERT: Wormholes and warp drives will not work, cannot work, are not physically possible (even though they are "solutions" to the EFE), would not be feasible even if remotely physically possible.

Not really. But it does imply weird things. Sabine Hossenfelder did a video on this.