That kind of system has the advantage of evening out the playing field with cars, where for a car you pay a massive upfront cost and then the marginal additional cost of each journey is so low that you get incentivised to drive even when buses and trains are perfectly adequate, or walking or cycling would be feasible.
The disadvantage is you're still disconnecting the price people pay from the actual cost of the resources used for each journey - which is always going to lead to economically inefficient decisions. Far better really to just charge people a reasonable price for each journey that reflects the cost of providing that transport, and also sort out a decent road pricing system for cars so that motorists also pay the appropriate marginal cost for each journey.
Capacity would likely stop people from taking short trips at busy times, when capacity isn't an issue then taking unnecessary travel wouldn't be an issue.
Yes you'd want to look at improving capacity, which would come at a cost, however some of that cost would be built into the numbers assumed.
For example the £5bn of TfL revenue includes income from their road pricing (some of which would disappear), however had nothing to do with how much it costs to run public transport.
Likewise, the £1bn of revenue at First Group would include some income from railways and possibly overseas - which means either I've double counted or it's extra money which I've allowed for which isn't needed.
That's before you consider cost savings (less station "office costs" and fewer staff needed - and even if you retain some for customer service or safety reasons there would be some savings you could deliver; for example a station with two ticket staff and a member of platform staff could see that reduce by one member of staff and still have a better customer facing service than currently) or other forms of income (rather than needing ticket windows and queuing space you could have another retail space).
That's assuming no cost savings from roads (less road building and less maintenance would be needed) and no cost savings from people being healer (walking to/from/between public transport stops).