What’s the history behind mercenary fleets and “sellsails”? My understanding is that private navies, requiring substantial and expensive infrastructure and so usually the preserve of monarchs, have been less common throughout history than private armies?

Less common, but certainly extant. So for example, in my research on the recent medieval naval warfare question, I found out that it was common in the Medieval ages to hire merchant ships as sellsails – either as transport ships or using the bigger ships that had some defensive capabilities built into them. 

Likewise, it was also common for naval powers – Venice, Genoa, Pisa, the Hanseatic League – to sell their services to other countries for economic considerations.