Note that even if you are limited to the HSAs your employer provides, you can still set up your own HSA with whatever trustee you want and periodically transfer the funds from your employer sponsored HSA to your own HSA: according to IRS pub 696 "Contributions to an HSA" section:
A rollover contribution is not included in your income, is not
deductible, and does not reduce your contribution limit.
Archer MSAs and other HSAs. You can roll over amounts from Archer
MSAs and other HSAs into an HSA. You do not have to be an eligible
individual to make a rollover contribution from your existing HSA to a
new HSA. Rollover contributions do not need to be in cash. Rollovers
are not subject to the annual contribution limits. You must roll
over the amount within 60 days after the date of receipt. You can make
only one rollover contribution to an HSA during a 1-year period.
If you instruct the trustee of your HSA to transfer funds directly to
the trustee of another HSA, the transfer is not considered a rollover.
There is no limit on the number of these transfers. Do not include the
amount transferred in income, deduct it as a contribution, or include
it as a distribution on Form 8889, line 14a.
There may be minimums, opening, closing costs, etc. or whatever depending on each plan, but that's not limited by the IRS.
So if you transfer the money yourself, you can only do it once per year, but there are no limits to when or how many times you can instruct the old HSA trustee to transfer funds directly to the new trustee. I also talked to the IRS today and they confirmed that you can have multiple HSA accounts as long as your total contributions don't exceed the yearly maximum (and from the quote above, transfers don't count as contributions).