Does entering Thailand visa-free require financial proof like applying for a tourist visa?

As I was not so long ago denied entry and sent back to Vietnam on the basis that I did not have 10k baht in CASH on me, they didn't care what I had in any account they wanted to see Cash, so I would recommend that you have 10k in baht per person, but also the 10k advised was when you only got 30 days on arrival so they could try and say you need 20k per person if they wanted to be funny with you.

Entering visa exempt has ALWAYS had a financial requirement. They can ask anyone entering visa exempt to show proof of 20,000 baht or equivalent in another major currency, in CASH ONLY.

They don't often ask for it, but it is a requirement to enter Thailand as a tourist. Whether that's with a tourist visa or visa exempt, you can be asked to show that cash and can be denied if unable to show it.