Occupancy restrictions are enforceable
Age-restricted communities operate under rules about the age of occupants and often about how many homes may be rented at once. Placing a tenant who does not qualify, or exceeding a rental cap, is a governing-document problem that can leave you unable to rent the property legally. No insurance product addresses that; it has to be checked first.
Minimum lease terms are common
Many such communities impose a minimum tenancy, frequently several months, which rules out short-term rentals entirely. That affects the whole economics of the property and it is set by the association rather than by you.
The association insures the common property only
Streets, amenities and shared facilities are theirs. Your home, your liability as owner and your loss of rent are yours, and the split is set out in the governing documents rather than assumed.