FWIW... the government information on medicare and supplements.
The only downside that I can see is the more variable changes in the Advantage plan price.
You correctly assumed that if you move, that a comparably priced benefit policy may not be available. According to the government publication, you may keep the policy you have, even if you move, or buy a standard policy. The Prices will vary by provider.
An important note for some... All policies purchased after 1992, are non- cancellable by the operator except if the company ceases to exist, if the information on the initial application was not true or ..... if you cease paying the premium. If you move, or want to change providers, you can do so with no penalties or increases due to prior conditions. (see page 35)
The publication may be worth reading for other questions on the supplements.