Automata Theory is a subject where we mathematically model a computing device and study the theory behind it. Here we group the computing devices based on the number of languages they can accept. Based on that we say :
Finite Automata's Power < Push Down Automata's Power < Linear Bounded Automata's Power < Turing Machine's Power
and hence forward it is a widely known fact that Turing Machine is the most powerful machine.
But my question is why do we say machine A is more powerful than machine B based only on its language accepting capability? I mean there are lots of other things that a general machine can do. Why not base the concept of power on those other things? In that sense a TM can do nothing more than accept a language!! Can a TM wash clothes? No. Because it has no capability of accepting the input (i.e clothes) on its tape. Can it produce heat energy? No. Because its output is fixed on pencil and paper.
At max, a Turing Machine can do all the possible mathematical problems. Leave alone the other ones like Finite Automata or the Linear Bounded Automata.
So what effectively do we gain by classifying the machines based on this particular property of expressive power excluding all the other properties?