I'm not sure what to think about it. My spontaneous feeling was also rather reserved, but then I don't really see a rational reason for expecting problems.
The City Car Club (as I understood) was a commercial company already, not a charity or something. Now a medium-sized company is bought by a large one, that happens all the time and I'm not sure why this should specifically be an issue here.
Do they really get "subsidies", or is it just a commercial deal between company and council? The council benefits and saves money as they reduce the demand for parking. A lot of other council activities are also contracted out to commercial companies. Cycle lanes are also built by big international construction consortia, not the local council workman.
In any case, providing hire cars is not a council service, but a commercial activity.
I can't see any ethical issues here other than one may not like big companies in general.
A practical concern may be that the service or usefulness suffers, but why should it? Enterprise has been successful in car hire so they should be able to handle hiring out cars (I would be worried if it was bought by L'Oreal to park their money or something without actual interest / competence in the business).
So I'm not sure what the fuss is about at the moment.