I think the logic should be as follows:
WHAT DOES A FINITE AUTOMATA DO?
It sees the input one by one and switches the states according to the input.
NOW HOW READ-ONLY TM equals FA and not even CFL?
Now the input tape can be just used to read the input and nothing else. And work tape can be used to simulate the FA rules and accept/reject the input.
Since the work tape is also constant size and not O(input size), therefore we cannot even copy the input to work tape.
With write capability off, we cannot even pop the inputs and hence CFLs are also not possible. But just provide tape with stack operations capability and then the TM will even recognize the CFLs.