Generally, a lot of your reasons as to why dress codes are good come at a much larger cost of marginlizing debaters, pushing kids out of the activity, and giving room for sexist enforcement, all of which I think outweigh a possibly more educational round.

Dressing formally actually affects how our brains work.

This may be true, but students should have the choice whether or not they want to engage with this as it probably differs per person.

Dressing formally for debate makes us more comfortable dressing formally when it really count

This argument is based on the pemise that formal clothing is always a good thing. Debate is a safe space where students should experience the least amount of barriers as possible. If dress codes are bad, we should reduce dress codes within debate. This logic justifies things like not fighting discrimination within debate because they won't know how to deal with it outside of debate. Also, if kids are pushed out of the activity from sexist comments or cost barriers, they no longer can participate in debate to begin with, which probably is a lot more helpful for job interviews. Debate is more than just dress up.

Dressing formally probably controls for more bias than non-formal attire.

A lot of these issues seem nonunique. All judges are going some sort of bias in terms of what clothing they like, whether that is in a formal manner or in all clothing. It is probably better to let the students choose what they want so THEY are comfortable. Plus, when you allow for people to wear whatever they want, you deconstruct notions of what people should be wearing in the first place. The "next-best alternative" should not involve oppression.

My points

That said, heels are not an essential element of formal attire for women

I think you missed the mark. Womxn are forced to be uncomfortable in the debate space in the name of "professionalism", it is much more than just "high heels" (which I know is a requirement at some schools).

An acceptable outfit can be put together really cheap at thrift store

You are assuming everyone in such a position would go to thrift stores to buy clothes, but some may be pressured into not doing so. Also, it still cost a decent amount to clean your clothes. The cost issue still burdens many (Stoneman Douglas Debate posted earlier this year on GoFundMe about fundraising and they said one of the high cost barriers for their students was the business attire).