These are some valid points, and I don't deny that you're certainly onto something here. In regard to each of them:

#1 - I fully agree with this. The fact that a pet cannot zone with you is annoying. While you can lower Call Beast's timer between the ACP body and merits, even so that still puts you with a lot o time to twiddle your thumbs if you have to zone suddenly.

#2 - As it was mentioned, BST can proc a lot of red WS. All it takes is the proper subjob; they have the skill in the weapons. They can also proc a lot of blue between dagger (Shadowstich/Evisceration, both natural), club (Judgment requires subjob but that's still 2/5 even without), Scythe (Spiral Hell), sword (Vorpal Blade with SJ) and Axe (All) Not to mention the wide capability for red triggers that /WAR provides. I think in terms of procs they're still doing pretty well.

Also, in terms of yellow procs there's a possible bit of a rationale behind why BLU spells work while pet TP moves don't. With a pet TP move, it's a natural physical ability, a WS so to speak rather than a spell. With BLU, they're magically recreating the effect after learning how it works, thus turning it into a spell rather than the WS aspect. Honestly I don't mind so much; if I wanted to proc greyellow I'd go /NIN or /WHM or /SCH on potential light/darksday pops. You just have to adapt to the situation.

#3 - Pet intelligence - Unfortunately this is a bit more annoying with the whole hate aspect, but it's not that hard to get your pet back, from experience. If that other mob isn't still hitting on your pet, simply heel it and put it back on the mob. Sure it costs you a few seconds and maybe a hit or two, but at the same time it's not hard to control.