Realistically, all of these could only slow the game down by adding yet another mechanic to keep track of in a game filled to the brim with them, while seemingly doing little more than giving their user a free shot with next to no consequence from return fire (peekaboo and poptarting) or putting them in grave danger of incoming fire from somewhere else (circle of death).
Also, experience from Living Legends (which I consider far closer to CBT and AS) reveals to me that poptarting and circling don't quite have the effect shown here; jumping in place leaves you horribly vulnerable to return fire from the entire enemy team, giving you basically one good poptart before you must relocate lest you blow a leg or a side torso on the next jump, while circling arguably makes you easier to hit because they're in a relatively stationary position (right in front of you moving in a consistent, predictable way), all you have to do is compensate for lag and projectile velocity. Peekaboo maneuvering is there, but it's nowhere near fast enough to avoid most return fire aside from LRMs.
Finally, Battletech just has never really focused on these sorts of maneuvers emergent in Mechwarrior, simply because Battletech is actually very different from Mechwarrior; MW is real-time with pilots whose reaction time is measured in the milliseconds, plus the most (yet somehow simultaneously least) maneuverable and disturbingly laser-accurate (you basically have to try to miss a weapon shot) depictions of 'mechs barring MechAssault, while BT pilots have one plan for the next 10 seconds in 'mechs far slower (yet, similar to above, more graceful in movement) than MW ever had, plus ridiculously high to-hit numbers that usually START at 8.
