Our ETLs always wear tennis shoes. Actually, my ETL-HR dresses up a bit 9 times out of 10, but the ETL-SF, ETL-LOG, and 2 of our 3 SrTLs all wear tennis shoes every day.
Now that I think about it, I'm pretty sure my STL normally wears black tennis shoes as well.
If I were you, I would dress as nice as possible right up until it has even the slightest impact on your ability to do your job. Function over form, imo. We all make jokes about the "dressy" people in our store, because they also often end up being the laziest/most hands-off.
I totally understand dressing up a bit in order to portray a certain image to vendors, guests, etc. but I think it creates a better atmosphere and TMs seem to respect leaders who dress in a way that allows them to be totally hands on.
...but then again, this opens up a million arguments about whether or not it's actually effective/efficient/appropriate for ETLs and STLs to be doing the "work of TMs" so yea...I have no idea what I'm saying at this point lol.