HFS can fly, swim, and magma-swim. They pathfind through every non-wall tile on the map. That's a lot of pathfinding. Strike them from the holy underground, and claim time itself as your slave
This doesn't account for the lag caused. Even if you did have all that pathfinding occurring, it wouldn't lag that much; if you did, large sieges of flying, swimming, magma-swimming creatures, like the FD Nightwings for instance, would cause similar lag, but they don't. In addition, they only do pathing once, then continue on that path until they're interrupted, so that wouldn't cause such a consistent drop as they cause, not to mention that they can't possibly be doing pathing to places they can't reach, as if you seal off Hell again with a drawbridge or similar the lag (eventually) disappears even if the clowns don't. If they actually pathed through every non-wall tile, well, sealing the paths wouldn't help.
The actual answer is that they all have the BUILDINGDESTROYER:2 tag, and so path towards every single building you've got, and probably repath to them every step. You can see this phenomenon with buildingdestroyer sieges, too, which also cause 99% FPS drops while they can path to all of your buildings. Since flying, swimming, magma-swimming creatures in large numbers due to siege don't cause massive lag, and buildingdestroyer creatures in large numbers due to siege do, the implication is that the large numbers of flying, swimming, magma-swimming, buildingdestroyer creatures due to HFS cause lag due only to the last property, not the first 3.