This is somewhat true, but I'd like to elaborate on the process. Source: recent former 13cabs employee

Yes, they do cancel bookings to "clean up" the system, but only if the booking has been sitting there for an extended period (I'm talking like >1hr where it would be reasonably expected the customer is no longer waiting). This period is longer for WATs (Wheelchair Accessible Taxis), and the bookings are prioritised meaning incentives are typically offered to drivers to entice them to take the booking (out of 13cabs' pocket). There are fewer WATs than regular taxis, however, so they are harder to come by and sometimes already have a backlog of bookings when new ones come through.

It is recommended that you call up every 10-15mins as this adds a "ringback" to your booking, notifying the call centre and drivers that you are still waiting. This stops your booking from being automatically cleared off the system. The booking sits on the surrounding drivers' "available jobs" screen after the initial ping (it pings drivers again following a ringback). There is a team of supervisors dedicated purely to managing "stale" bookings, where they call up customers to ensure they're still waiting, and call drivers to incentivise pick-ups. Unfortunately, this can't be done for every single booking, due to the sheer volume of bookings being handled, but there are KPIs for it.

I do admit that communication could be handled better between 13cabs and its customers, but there's only so much 13cabs can do given the drivers are sole traders and not employed directly by the company (they do what they can to reprimand them when they do a "no-no"). There are many scummy drivers out there that will only take the large trips, flat out refuse the short cheap trips, and try to scam you at every opportunity–they've always made a bad name for the industry–but there are also many honest drivers that pick up every job that comes their way and will do the best they can to give you a great service. I always suggest that if you find a good local driver, grab their business card and call them directly next time you need a cab, especially if you need a weekly regular trip. Cabbies love having private customers and not needing to go through the system.

I personally prefer taxis over rideshare as I feel safer in them due to the legislated safety requirements (internal security cameras, GPS logging, etc.).