What are the benefits of *rigid* lefty fork?
One obvious advantage for most lefty bikes is


You’re able to change the tire and tube without taking the wheel off the bike. So wheel adjustments and repair can be made without interfering with the disk brake rotor. This is especially useful on rear wheels as you also don’t have to take off the chain.  


In the case of these rental bikes, I suspect that the real reasons are:


Most everything on these rentals that can be made non-standard is — from the head tube diameter to the axle width. This slightly lessens the risk that the bikes will be stolen to be stripped down for parts. 
Branding and theft reduction: The bikes are highly visible and recognizable even if they are repainted