I agree when you say that the hat system makes you diversify classes ...
But I also believe the Random Drop System also has a mind of it´s own, just like AI Director from L4D.
One fine example of this, is that I accidentally deleted all my kritzkriegs last week... I´ve been getting items more or so regularly, but never a kritzkrieg again...
Also I don´t have a single hat....
I play all the classes when they are needed with the exception of the solly which I totally can´t stand... Hell I even press that Random button every now and again

Cheers