Philip bowing was part of his job working for the 'Firm'. Do you really think he did so off duty?

What is common between Philip and Melinda is that they both worked for the firm which was under the control of their spouse. Melinda was a Microsoft employee at the time of marriage to Bill. Queen could at any time strip away the title of prince from Philip just like she stripped the title from her Son Andrew amid sexual abuse lawsuit, despite the alleged incident happening when Andrew was off-duty. Likewise, Bill had the power to hire and fire, influence salaries and bonuses etc. Do you think there is no power imbalance between an employer and employee?

As for the Gates, didn't Bill make most of the money? Yes, with his wife's support, but still he did the work

Exactly, you are making the argument which I am trying to give. Bill had more money and was also more influential being Melinda's employer. With so much influence ,he could even afford getaways with an ex-girlfirend despite being married to Melinda.