It has been a huge improvement in places like Manchester which the OP mentioned has switched to the London model. Before it was unbelievably expensive and fragmented in terms of the service with different providers requiring different fares or weekly/monthly passes. Also never knowing when a bus was going to show up.
Now their an app which shows you when your next bus will arrive tracked by gps so you can leave the house on time to get there, and fares are standardised at £2 per trip or £5 all day.
Before the standardised pricing you had people on minimum wage who would be paying an hour or two of their wage just to get to work.
All this came due to the local Government mandating it, these things could have been implemented before by private companies as they have existed in London for years but they simply chose not too.
As a former Mancunian, this was the city I was thinking of.
I remember having a meeting about a completely unrelated matter with TfGM many years ago, and they bemoaned not having the same sort of sway as TfL to fix public transport - buses in particular.
The bus situation was madness for decades: there was weird operator specific passes on the Fallowfield/University corridor (the busiest bus route in Europe when I was a student there), so you had to choose at the start of the week if you wanted a Stagecoach or a Finglands pass and then you were stuck with it. The North/South operator divide meant that everyone trying to get from say Cheetham Hill to Rusholme, had to pass through Piccadilly Gardens because that's where different companies "owned" different stands. That just led to all the problems of... well, Piccadilly Gardens...
I've not tried the Bee Network myself yet on any of my recent visits, but it looks like the fix that was needed, and it sounds like they have at least one happy customer in you. I genuinely believe it will contribute to better working conditions, cleaner air, and even economic development for Manchester.
And all it took was fixing the buses, something everyone knew needed doing more than 20 years ago...