Is it sensible to enter Thailand on a tourist visa and then apply for a retirement visa while in the country?

Honestly your best bet would be to get a year long, multi-entry Non-Immigrant Type O-A (Long Stay) visa from the thai consulate in the US before you wing your way here. That way you can use your income in the US to meet the proof of funds. When you get that visa and enter the country you will be stamped in for a whole year (or as long as your health insurance is valid for up to a year)

You want the O-A visa from here:

/30/nonimmigrantoaox/

as an american there is no way you can show "proof of income" that will be accepted here at the immigration office to get a Non-O visa or a year extension. The US consulate hasn't issued income from abroad notary documents since Dec 31st 2018 :O

That means you have two ways to meet the proof of funds to get a "retirement visa" inside the country you bank 800K baht in a thai bank account in your name only for 2 months before you apply for the year extension

OR

You transfer IN to the country in a thai bank account in your name only from abroad a minimum of 65K baht a month each month every month for the preceding 12 months before you apply for your extension.