Healers have disliked death knight tanks for as long as I can remember, going all the way back to I think it was 3.1. When DK's first came out, they were known as a cooldown tank - basically they would fill out their trees so that they were able to chain one cooldown after another to create a long string of mitigation through cooldowns. Then they made some changes to the trees, and the specific abilities (RIP beast mode Lichborne), at which point DK's were squishy as hell, especially against adds. They fit a niche throughout the rest of wrath as the "magical tank" due to AMS, but the overall issue with them was, without a shield, they were completely awful at dealing with adds. This also made them hella squishy against basic trash packs.

Your average DK tank will have a much easier time tanking a solo boss without any adds, than he will against a 3-4 trash pat.

The other problem (that is mostly okay now) was when threat was an issue. DK's had similar problems to warriors with adds and trash in that it took a few global cooldowns to get aggro on an entire group, and healer aggro or dps aggro was common. With the changes to death and decay costing only one rune, and the threat modifier buff, this isn't so much of an issue, but I remember at lower gear levels, it could be tough. You had to really choose between threat and survivability at times, and that could be a really tough call back then.

This all being said, I've at least dabbled in each tank spec that is out there, and DK tanking is by far the most fun to me. That may be because it feels more like a DPS rotation, swinging a big 2handed axe death striking for huge crits, not using things like Holy Shield and whatnot, so I would hope that whatever blizzard does, they make it as fun for Bears as it is for DK's.