Some counterpoints:
a) The addditional transport volume means more energy consumption. It is possible that this is offset because less items need to be manufactured, but given that many items expire with use (i.e. your vaccuum will break down after X hours of use) this is unlikely.
b) You've gotten used to your brand of vaccuum, how to empty it, how ling the cord is etc. Doing Rental means you are going to get a new unit moreoften than if you own one, and it means there'll be a (short) period to become comfortable with that.
c) You still need manpower to check that returned rentals are in good condition or risk frustrated customers.
d) A good location to pilot such a service would be a high-rise apartment building or complex. If this was profitable, why isn't it done today?