I agree with the spirit of what you are getting at.

Except that it's not fair to simply assume that a good salary was roughly similar in terms of purchasing power across the a few centuries. In fact at that time middle income people were much poorer in terms of what they were able to consume, purchase, and barter.

As one example, the power loom didn't exist until the late 18th century. Before then, clothing was really expensive because an unbelievable amount of hand labor had to go into it. The average person did not own a lot of clothing, and the clothing they did have cost them relatively a lot of money.

Which is also where the term "selling the shirt off your back" came from. Back in the days when clothing was worth a lot more, you could actually trade your clothes for stuff in a pinch. Nowadays clothing ain't worth much.

I finally get to ask someone directly: in “the a few centuries,” are the two articles considered valid English or is it a mistake?

It is a mistake.

It's a mistake

Phew!

Now for the mystery of “the the” which I sometimes encounter...

I would assume a typography error unless it is a band name. I've typo'd "the the" more than once.