At one moment you said that tactical jump was fine when BC was balanced differently ; and the other you say that tactical jump will always be a problem on the BC because of characteristics the BC did have since 2010. You are contradicting yourself.
Iâm starting to wonder if whatâs disturbing you isnât the TJ in itself, but the fact BC became a viable, regularly used unit .
An opener being capable to deal damage enables it as an harass timing, or timing push. Having more openers usables as harass/pushes implies more gameplay diversity, and is on the contrary good for the game. 
Well you must be a curious individual then, because I merely reused the comparisons you yourself provided. 
It is when you classify the counters as soft and hard, and by relative abundance at the unitâs timing. Vikings are common most TvT compositions. Blink stalkers, corruptors and hydralisks are common in TvZ and TvP as well. Only Tempest, though not rare, isnât that often produced in TvP.
Coming from there if an unitâs hard counters are already common on the battlefield, producing the unit is a mistake ; specially if itâs a T3 unit. Hence, why the BC was never used prior to TJ, and never used in harass prior to TJ and fire-while-moving ability. Proof being that itâs still never used as an opener in ESL level TvP : because of the relative abundance of stalkers compared to BCs at that timing would make BCs production a mistake.
If you think about it two seconds, if you removed the tactical jump and let it at that, there is just no way the unit would be viable against Tempests, nor corruptors; nor infestors, nor vikings. And that because contrary to most T3 (carriers, tempests, colossus, HT, BLs, Vipers and Thors), it just doesnât have a T3 range. And so if you want it to remain a slow moving, short ranged unit, it just needs an escape spell. 
Now it could be discussed :
- to trade the escape spell for a T3 range (but that would break its vikings counters, so unless you want to increase vikingsâ range proportionally, which may induce other issues, itâs not really an option).
- or to keep its short ranged T3 design particularities, but to tweak the balance of the viability escape spell :
â Keep the teleport, but nerf its timing (research necessary) or cost, its downsides (4s vulnerability state just like recall), or its availability (shared cooldown with yamato).
â Or transform it into some kind of non maneuverable afterburners (same speed than a corruptor, midmap range), but in return slightly increase its ATA dmg to compensate (5->6-7).
From the moment the objective is not to return it to a non viable/unworthy state, lots of balance tweaks who could be discussed. 