My spouse and I both grew up in this kind of household. Interesting to see how we & our siblings all responded, some followed suit and others had opposite reaction. I think some people are good at frugality and some are good at income maximizing, and few are good at both.

I turned into an income maximizer.. started working at 14.. post college left home, took a high stakes career and hopped to new opportunities proactively. Response to not wanting anyone to be able to control me via money.

For my spouse & I it was a reaction to 1) having a lot of childhood of consequences/regrets of over-frugality like frozen pipes bursting, parents lamenting not going back home for 10 years during which their own parents died, asking for a single $10 toy for birthday and having them buy a knock-off instead, etc.

2) a reaction to teenage parental control via money like when I was moving to the big city for my job and the housing deposit was due before the hiring company was going to wire me my housing stipend, and my parents refused to float me $1k for a month (and then gifted me more than this as a graduation gift a few months later).

So I think you want to instill a respect for money in your children but not a fear.