They never do them by referenda because they wouldn’t like the result. The Jamaican political class have been trying to make Jamaica a republic for years but given how much they are despised by ordinary Jamaicans and opinion polls suggesting many would rather have stayed a British colony they know the Jamaican public would use a referendum to explicitly reject a politicians republic.
In the case of Barbados and for Queen Elizabeth, you are 100% correct
Queen liz is a good Queen of Barbados.
Quite frankly any current realm with liz as Queen does not want to see her go - she is regal, she is impartial and she is honorable. Once she goes things may change, but not before