The only tightwads here are the businesses (and the employees who agree with their policies) who will not pay their employees a fair wage. Again, it is not the responsibility of the customer to ensure that a business survives and thrives. My question to you is "Are you a business owner who does this and are now trying to justify your actions?"
So, you are in agreement with the customs of other countries that women should be treated as second class citizens. You are espousing the treatment of employees by their employers as second class citizens. Your comparison to shoe removal in Japan is not even in the league of the social injustice attitude of not paying employees a fair wage.
In my country, tipping is not the custom as we have minimum wages to adhere to and if a business doesn't do this, those in charge are prosecuted.
Finally, I have no intention of ever visiting the USA. The way its citizens are treated is appalling enough, how it treats its visitors is even worse.
I don't have the personality to do this - I am considered to be far too blunt and abrasive. Yet, even though I am this, I consider it extremely important to treat my clients in a manner that says that I will solve their problems and actually do this. None of this work ever involved tips, it was a part of the service that I thought necessary.
I'll go further: if you are visiting a different country you should make an effort to adhere to their basic norms of behavior. If I go to Japan and I see a shoe rack at the entryway of a building I am not going to traipse around the building in my shoes, even though nobody would think this behavior was unusual at home.
Also, if I were going to carry out your policy, I would not plan on visiting the same restaurant twice.