The thing so many on this thread are not realising is that anything 'cheap' comes at a very real cost somewhere down the food chain.
The running costs of a Black cab vs an PHV are significantly higher, insurance is sky high and as few seem to understand, the rates charged by black cabs are entirely governed by TFL, not the drivers.
The assumption that a satnav is somehow a substitute for the knowledge is also very short-sighted. For instance Selfridges has umpteen entrances, the Tower of London is best accessed at the gate where the ticket office is located, Museums and galleries have different exhibitions and theatres have changeable shows, these are all instinctively known by black cabbies, but not PHV drivers. Knowledge points that black cabbies are required to know are far ranging and reaching and set the bar far higher than jumping in a cab asking for TrafalgarSquare and the driver asking the passenger "what is the postcode"?
Many tourists book what they believe to be an hotel in Central London, but in fact it is outside -black cabbies know this , PHV drivers don't.
Then there's the vetting of drivers which Uber have so woefully managed. There have been hundreds of PHV driver registered who allow family members to act as a driver. This means that those of you honestly believing that the tracking details you receive via an app does not always translate to the person driving you home, who has then obviously unknown to you, Uber and entirely unchecked. You would never be able to determine whether they hold a valid passport, never mind a criminal record.
Medical checks have been found in high numbers to have been fraudulently issued under the lack of management of Uber's own system and this of course means that your driver may well be unfit or unlicensed. Or both.
Then there's maintenance; a black cab requires very stringent annual checks on top of an mot and other annual charges. This is not issued unless they produce valid cab insurance. However, because Uber have failed to check, many PHV'S have had their car registered, produced papers and then 48 hours later cancelled and amended their insurance to normal car insurance. This of course means that if you are unfortunate enough to be in an Uber who crashes, then you are uninsured.
Then of course there is the issue of fare surging which has been acknowledged by Uber as a problem.
So, OP in answer to your question, the "point of black cabs" is precisely what it always has been. London's finest, checked, triple checked with an exemplary record and drivers who actually know the difference between the Thistle Tower and the OXO Tower. They are also a bloody godsend if you happen to be disabled, infirm or have no knowledge of our great city. They took folks to home or places of safety during the London bridge attacks and did the same in other tragedies.
They and their prices represent the service they provide, like any other, you get what you pay for. if you don't like their prices, take it up with TFL.
Uber were arrogant enough to think their global clout would make them above question, they fell foul and will have their work cut out to overcome their now "not fit and proper" tag, but am sure they will manage it somehow via their usual methods.