I've tried to reach a point were the pet could use its basic attack on cooldown (3s) but it seems like it's impossible, even with absurd amounts of haste (1315%) your tool only go down to 3.28s.
Is it due to a possible bug or is it because pets have a slight delay before they use an ability?
With the BM profile linked above, the frequency of basic attack is 3.41. Does it mean that Frenzy/Focus Fire and Invigoration won't scale (much) with gear?
There is a known issue in game with pets where they won't send the request to use their next basic attack until after they've gotten confirmation from the server that it's off CD. So even when full on focus it won't happen more often than every 3.3 sec on average (this actually varies a bit depending on latency and stuff in game, but based on log analysis, 3.3 sec seemed a reasonable average to use for simulation).
If you wish to turn off this behavior you can check the "Don't Emulate Known Bugs" option in the settings- currently this is the only bug I support via this setting.
Well having more regen will mean you will have less basic attack delays, it'll also mean you can perform more wild hunt attacks. But there's definitely a practical limit on how much you can increase your Frenzy/Focus Fire and Invigoration. Keep in mind that when we hit 90 our regen will go down as our gear won't be as good relative to level (which means we'll need more haste rating for the same amount of haste) so it'll be harder to maintain minimum basic attack delays.