I don't think it is as much about profitability but more like who should pay for it. In one world view, the people who use it should pay for it, whatever that costs, in the ticket price. This gives direct pressure to keep costs down.
Another view is that it mostly benefits people in London so it should come out of London's Council tax (which I think part of it does).
The other view is that it is a general benefit to society and can and should be bankrolled by government. Then the problem is that the pressure to keep costs down is perhaps political and it is hard to know how much subsidy is fair.
TfL is funded from fares, the congestion charge, business rates and grants from the Greater London Authority — which itself is funded by the national government and some council tax.
It mostly transports people who live in the 'home counties' (the smaller towns and countryside surrounding London) to and from the major rail stations, so maybe they should pay for it. e.g. 750,000 people pass through King Cross station in the morning rush hour.
At the same time there are benefits to nontransit users having a chunk of the population use transit. The roads are clearer, for one. Less smog, for two. Higher national GDP due to less resources overall required to move labor from housing to the means of production, for three. I'm sure there are more reasons, too.
Another view is that it mostly benefits people in London so it should come out of London's Council tax (which I think part of it does).
The other view is that it is a general benefit to society and can and should be bankrolled by government. Then the problem is that the pressure to keep costs down is perhaps political and it is hard to know how much subsidy is fair.