Metro Bike Share is run by Los Angeles County. Not the city of Los Angeles.
There's no reason why they can't fund a separate system. Metrolinx already provides funding for Hamilton's separate system. There's just no good reason for Toronto's municipal government to be running bike share services in another municipality, especially when it would require a small operating subsidy from TPA.
And I don't think anyone buys the "last mile" argument. Not when you need to buy a long-term membership or pricey day pass and all of the bikes are in the part of the city with the best transit coverage. Bike Share is meant to work as an alternative to transit, because in the core it's often just as fast (or faster) to bike as it is to take a bus/streetcar, and the cost per trip is lower with the bikes than the TTC.