I wouldn't say mutually exclusive. Inherently a good tank at present can make healers' lives easier by mitigating more, but the real focus (or so it appears) is on them dealing more damage, as opposed to mitigating more, which brings me onto my second point below.
This is the biggest issue (in fact, 2 issues) in my opinion. The first is that there is no gearing choice. Despite there being a tank stat in the game, the benefit is so negligible (especially due to the current progression favouring magic damage) that it's not worth taking. The second issue is that damage comes in predictable spikes to mitigate, rather than consistently. The upshot of this is that experienced tanks need only use their tank stance to open the fight and then at set points in the fight for a tank buster, elsewhere they're DPS. This is probably personal preference, but I would prefer if damage had spikes, but there was consistent high pressure (this may be the case already - I've not been in savage, but as I understand that is mostly spikey) which would need tank stance to survive.
Yep, that's also the case with SWTOR. Enmity generation is, to a large extent, locked behind abilities which can either only be used in tank stance, or which have additional effects. It also ties defence (shielding, defending/evading and generally having double the armour value (going from about ~20% to ~45% passive reduction)) to having a tank stance on, meaning if you attempted to tank without it, you could manage a couple of hits, but will die fast and lose agro unless an actual tank gets the boss back off you quickly.