First lets take a look at a comparison between Annie, and a tankier character with similiar abilities. (Leona)
Base Health at level 18: 1752
Base Armor at level 18: 84.5
Base MR at level 18: 30
Base damage at level 18: 96.25
Base Health at level 18: 1996
Base Armor at level 18: 73.8
Base MR at level 18: 52.5
Base damage at level 18: 109
So by straight base numbers, although Annie does have more armor then Leona by level 18 Leona has a much more balanced scale ending with more health and MR. Leona will have more Armor than Annie until about level 10 which puts her at a good early game situation to be there for her carries and take more damage early game. In terms of item choices it tends to be easier to find items that fit the bill that buff armor and other aspects of your character than find items that buff MR.in late game so her armor deficit VS Annie will be less crippling by then.
Utility: Leona has multiple stuns (All of her spells but shield) that can be used on a whim with no waiting for a passive CD/number. Her lance is great for iniation because it puts her right in the heart of the battle from brush or straight on. Also, her passive can stack a giant enemy crabs level of damage onto opponents. So I would say overall Leona adds a more dynamic aspect to a team giving them great CC and bonus damage output.
Example: Her Lance,Shield,Ultimate combo basically ensures a wonderful initiation to any team comp. Keep in mind that sunlight is consumed by many skills. Example: If Leona used her lance and timed the shield well then a teammate (Ashe for example) vollied and consumed all of those markers then her ult goes off resetting them for Ashe to volley again consuming those as well.
Sustainability: Her Eclipse grants her +70 armor and magic resist which if used properly lasts for 6 seconds. On a 14 second CD that leaves her with 8 seconds of downtime between uses. So slightly more time down than up, but the benifit is great combined with the sunlight it applies to all enemies. Not to mention as said before her base stats overal favor her in the long haul with MR and Health and they also favor her a good portion of the begging and midgame in Armor due to scaling.
Overall: I would not say that Annie is nesesarily a bad choice for a tank, you prove some good points. However, I do feel in a realistic scenario a champion more suited to tank like Leona will really bring more to the table for the team overall.