Not having played any other MMOs (TOR is my first), I find this sort of thing surprising.
What would be the benefit of ignoring weaker mobs and having the DPS focus on the tanks main high-health target?
It would seem that even in other MMOs, a weak enemy is a) Still capably of doing damage to the party and b) Dies relatively quickly so why not kill them immediately?
Do killing the weak mobs give a buff to the elite mob (like a mini-enrage)? If you kill weak mobs do they respawn with more of them (herakles and the hydra)? Do every elite mob come with a tight enrage timer so any time dps'ing trash is bad?
Ok, there are a few fundamentals you need to understand when comparing SWTOR tanking with more "traditional" tanking styles that had been in MMO market for years.
1) In games like WoW, the only place you will encounter "Elite" mobs are in dungeons and raids. There are a few that wanders out in the open world, but they are generally World Bosses, Town/Outpost guards, or Special "Outdoor raid" areas similar to Heroic areas in SWTOR. The Elite mobs will have decorated portrait frame, just like SWTOR.
2) In other MMOs, there are typically 2 types of "Elite" mobs: "Dungeon Trash mobs" and "Bosses". Rarely in a dungeon (Flash Points) will you find regular mobs in games like WoW. Important thing to note here is that all Trash mobs in other MMOs have generally universal HP pool, so there are no "weaker elites" or "stronger elites" in terms of HP. To put it in SWTOR terms, imagine every mob in a FP is an Elite class, walking around with 40k+ HP.
3) The most important concept you must also grasp is how the mobs are scaled in these games. In games like WoW, Elite mobs are designed in the way that only Tanks who are spec'ed and geared correctly are able to survive their attacks. No ifs, ands or buts. If you pull threat as a DPS or healer in those games, you generally will get 1 shotted, unless you are using defensive CD or if you are wearing heavy armor and such. In those case, you might get 2-3 shotted. Bottom line: If you pull threat, you will die very, very fast. So in those games, the core mechanic is designed around the Tank being the sole focal point of incoming damage, who in turn will stack mitigation/avoidance stats through the roof to survive the onslaught. This, of course leave very little "offensive" stats for Tanks, hence in games like WoW all tanks are automatically given 500% threat increase for ALL their attacks as long as they are in Tank stances.
4) Other main difference is how the resources are different in SWTOR and other traditional MMOs. In traditional MMOs, typically all healers uses a resource called "Mana" or some variation of it. They are like Force bar of Sages/Sorcers, except they can be increased from gear, rather than fixed at 600. Also the way which Mana regens works very differently compared to SWTOR. So even though healers can walk around featuring 300k+ Mana points, they WILL eventually run out if they are forced to divert their resources over multiple targets. So in a game like WoW, if you pull threat as a DPS, not only you are putting yourself in danger, you are wasting precious resources from the healer who then has to worry about you and healing the Tank.
So from the above points, you will see how the difference in fundamentals will get veterans from older generations of MMOs confused about how the roles of Tanks and DPS operates in SWTOR; because unlike in SWTOR, in those games there are no mobs in Dungeons (FPs) or raids (OPs) which a single DPS can 1-2 shot normally.