What are the benefits of *rigid* lefty fork? I know there is already a discussion about suspension lefty forks. However, that post completely avoids mentioning of their rigid counterparts which also can be found in the wild.

Below is a couple of photos of rental bikes commonly used in Singapore.





[While looking closely at the second picture, I have realized that there is also just one rear dropout!]

Searching through the net gives other examples of rigid leftys:





EDIT Added more examples.

Vintage 1910's bike:



Somewhat's newer one:



So, what's the deal with them? What are advantages, and there must be some disadvantages (like less compatibility with fenders, hubs, rim brakes etc.)?
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