Why do we use single tape Turing machines for time complexity? As you know there are many anomolies for the single tape Turing machines when the time is $o(n^2)$: multi-tape TM simulation, simulation of larger tape alphabet with just $\{0,1,b\}$, time constructability, non-tightness of time hierarchy theorem, ...

Also results like $\mathsf{DTime}(o(n\lg n)=\mathsf{Reg}$, and very model specific $O(n^2)$ time lowerbounds for simple problems (that don't translate to even superlinear lowerbounds on two tape TMs).

For space complexity, we use a model where we have a separate read only input tape, which is more natural and robust.

A TM model with multiple tapes (or at least 2 working tapes) would be much more robust and will not lead to anomalies like those I listed above. I once asked a prominent complexity theorist who has proven simulation results in the early years of complexity theory if he knows any improvements on one of these old results and the reply was that he doesn't think that "questions about the one tape model are that important".

If we change the standard model for time complexity to a two tape TMs, reasonable results in complexity theory will not change and we avoid these anomalies caused by particular model. So my question is:


  is there any reason why the time complexity is still defined in terms of single tape TMs?
  (other than historical reasons)
I've seen texts define TIME( $f(n)$ ) using multi-tape Turing machines, but Sipser uses a single tape machine.  You've almost surely first encountered this material through Sipser because it's so fabulously well written.

There is a crystal clear pedagogical reason why Sipser does this, namely the course just naturally flows that way because :


You should introduce the single tape machine before the multi-tape machine, otherwise steepens the learning curve.
There is no compelling reason to introduce the multi-tape machine before introducing O($\cdot$) and TIME($\cdot$) for single tape machines.
You should ideally compare the multi-tape machine with the single tape machine the moment you introduce the multi-tape machine, otherwise the prolonged ignorance will lead to additional confusion.
You could omit introducing the analogous TIME classes for multi-tape machines, thus simplifying notation overall.


There is no reason to quibble over conceptual cleanliness when the pedagogy so clearly dictates the easiest path, and every computer science undergrad must take this elementary course, including all those who still don't understand proofs.