My understanding is that TML is polynomial in the size of the model, but the size of the model needs to be compiled to a given problem and may become exponentially large. So, at the end, it's still not really tractable.
However, it may be advantageous to use it in the case that the compiled form will be used multiple times, because then the compilation is done only once for multiple queries. Also, once you obtain the compiled form, you know what to expect in terms of run-time.
However, I think the main reason you don't see TML being used more broadly is that it is just an academic idea. There is no robust, general-purpose system based on it. If you try to work on a real problem with it, you will probably find out that it lacks certain practical features. For example, there is no way to represent a normal distribution with it, and lots of problems involve normal distributions. In such cases, one may still use the ideas behind the TML paper but would have to create their own implementation that includes further features needed for the problem at hand. This is a general problem that applies to lots and lots of academic ideas. Only a few become really useful and the basis of practical systems. Most of them exert influence at the level of ideas only.
