Okay, let's get through this again.
Tessellation is basically a dumb algorithm in all its implementations that can only "smooth" out a surface. The simplest way to imagine it is to take an 8-sided circular shape - as its divided to 16, then 32 and then 64 segments, it gets progressively closer to the perfect circle.
There are theoretical and practical issues with this process.
First, it smooths everything, so extra polygons have to be added to keep sharp details. This takes considerable artist time, and increases the base polygon counts (and every extra polygon gets tessellated and rendered, too).
Edge creasing can be introduced but it's not a reliable or all-around solution either, and makes iterative workflow very hard.
Second, perfect smoothness is completely unnatural, no living creature is like that. Characters in particular are designed with very complex forms, lots of various extra pieces and elaborate costumes. Think any space marine or fantasy orc. Also, any type of anatomy (faces, bodies hands etc) has incredibly complex forms and shapes, once again no use of smoothness.
This problem can be somewhat remedied by displacement mapping; this is basically offsetting each individual vertex based on a texture map, thus modeling a more complex 3D surface at rendering time.
But extra pieces like pouches, belts, spare clips, armor etc. can't be displaced from a smooth surface so this technique is most useful on stuff like dragons with horns and scales.
However proper displacement requires a lot of vertices, since the texture pixels have to be mapped to them at least 1:1. Today it's very common to use multiple 2K maps per character so you'd need at least 5-10 million vertices at least (and thus, the source models for normal maps are in that range).
This creates a problem with today's GPUs because they're not efficient at rendering small polygons at all. I'm also not sure how many vertices the GPUs can push through tessellation - Crysis 2 performance issues suggest this may be problematic at the very least.
So, in the end we have workflow issues, artistic issues, and technical/performance issues, all of which for a questionable quality result. Thus in the end it's far more efficient to manually add extra polygons where they count, and use discrete LOD models generated automatically by content creation software.