Say your bag is divination.
Divination is a functional grouping; you could have Ritual (Divination) or Thaumaturgy (+1 Divination Complexity), for instance.
I can see that having the right information allows you to solve seemingly impossible problems, such as tracking a person who left no trail, could be used for summoning spirits for the purpose of gaining information, etc.
Tracking spells are a subset of divination. Summoning is a different functional grouping, so divination bonuses usually won't apply. You could easily skin a divination ritual to look like calling up a spirit for information, but you couldn't bind the spirit to do a task.
Will your methods possibly become more convoluted? Yeah, probably, and will you be incapable of doing some things? Yeah, definitely, but you don't have to be anymore restricted than any other theme is.
Again, divination is a function, not a theme. The terms aren't interchangeable. See YS284, "Thematic Thaumaturgy."
I feel like this is why someone with full blown Thaumaturgy can have both function and theme specializations.
This is certainly possible under the RAW, though sometimes very slightly suboptimal, since your bonuses will overlap at certain points and won't stack. By far the best example would be a character with thaumaturgy who has a particular theme (say, Biomancy) and also some bonuses to Crafting, which is a function, because Crafting bonuses are unique in type. (He might have a specialization pyramid like this: +3 Biomancy Complexity, +2 Crafting Power, +1 Biomancy Control.)