I work for TfL on the tube abd have done for 20+ years. Here are my thoughts and knowledge on the matter.
For a few years before the pandemic in 2020 all Freedom pass holders could use their cards at any time on TfL services. This is because Boris Johnson,(who was Mayor at the time) said it wasn't fair that older people had to pay to get to hospital appointments. The OP is correct.
BUT the Freedom pass isn't funded by TfL it's funded by London Councils. Initially the ban before 9am (not 9.30) was to reduce traffic on the TfL network to reduce risk during the pandemic. However, since the risk eased councils were given less and less money from Central Government they had to keep the ban in place to save cash. It has nothing to do with TfL's crap bargaining with the DfT.
In my opinion most 60 year olds in London work be it in low-paid occupations all the way up to executive roles. So I think the minimum age should be raised to 65. It's galling to see some working 60 year olds who are obviously wealthy get free travel whilst customers on average wages have to pay (and season tickets are flipping expensive too).
At my area of stations, the Twirlies will turn up at any time from 8.30am onwards and wait on the unpaid side until the click ticks over to 9am then they all rush forward to the gate. Sometimes we get 20+ people waiting, and they moan about waiting to each other. It's the same faces day in, day out. I work in a wealthy suburb, like, £5m pound houses and posh shops on the main street, most of the kids go to private school, and these people reek of entitlement. It must be different in other parts of London where having free travel is a lifeline but where I am I think means-testing wouldn't be a bad idea.
Finally a load of Freedom passes were cancelled last year because TfL found a lot of older people who lived mainly in foreign countries but kept a house in London were claiming the Freedom pass. We had loads of older people coming back from their winter in the South of France or wherever and finding out their pass was invalidated. That caused arguments. All I could do was ask them to ring up the relevant number to sort it out. They should have got emails confirming their main residence was in London but some ignored it or didn't think it was important so lost the benefit.