HSA Account Question

That said, the employers I’m familiar with have said that you need to be either on Medicare or their coverage - not both, so again, it wouldn’t be possible if those are the employer’s rules.

Made me go look it up for my employer (only one I have easy access to their FAQ)
My employer does not have any rules that you can’t have HDHP coverage on a dependent that has medicare. And they do have explicit Q&A about a spouse/dependent having medicare and covered by the employee’s HDHP.

if there is an extra charge for family coverage (like all of the employer coverages I’m familiar with)

My employer does not charge more for family HDHP vs. individual HDHP.
(And while my employer has good health insurance coverage, I know there are others that are even better)

“I think they could potentially keep the family coverage HDHP and keep contributing to the HSA the family amount.”

If the family coverage costs no more than single coverage, and the employer allows it, yes. But if there is an extra charge for family coverage (like all of the employer coverages I’m familiar with), then it probably wouldn’t be.
IF they have to pay an extra charge for family coverage, that would not preclude that they could keep family coverage and keep the HSA at the family amount. It would change the balance of whether it’s worthwhile to do so.

Personally, I’d rather have $4800 in a taxable account, rather than paying $1200 to be able to put $3600 into an HSA.

Sure.
OTOH, if it’s $60 extra for the year, I may be willing to pay the $60 and have an additional $3600 in HSA vs. having $3660 in a taxable account.