I think car usage will stay higher until a while after Covid-19 has completely gone away. I will be hanging on to my car. We used to go to Cardiff from London by Coach. I will never do that again until I am VERY sure that I will not catch Covid-19.
I drive to work and now make a long detour via my partners work. Her boss has made her working hours very flexible to fit in with my times. She does not drive but if she did we would be buying a second car and using it.
My feeling is that currently anyone who has a car is using it so as to avoid public transport - central London excepted probably. I have noticed that traffic in Croydon is getting worse than the same time last year.
What I find stunning is that, at a time of crisis, London is planning to extend the ULEZ out to the North and South circular roads. With peoples fear of public transport that is only going to cause even more difficulty.
While Covid-19 is at large any reduction in peak time capacity would be very unfortunate as people need to distance more. For myself I gave up commuting to London so as to avoid the inhumane conditions - particularly on the tube. So any increase in space would be welcome.
So as far as central London is concerned I voted with my feet and avoid it. I think that maybe we are going to witness London becoming unsustainable as a work place ?.
So to answer the question "can public transport ever recover from COVID-19" I think the answer is no. I think people will go for quality of life.
There's two different times, the first which you directive in your post which is likely to be with us for another (say) 9 months until a vaccine can be rolled out and/or Covid-19 has run th through the population (whilst at 500/100,000 it'll take 200 weeks to infect everyone, however once it's got to 60% then it's going to drop away a lot, so likely to be about 120 weeks; and if there's any significant number of people who show no symptoms then it's likely to be quite a bit shorter).
The second is likely to beyond 2022 where things have returned towards what we had before (although it's never going to be exactly the same as some things will change), which is where overall travel is likely to be lower and therefore rail could well see passenger numbers back towards 2019 levels. Yes it may be 2035 before the levels get back to 2019 figures, however it should be remembered that a 20% fall would only roll is back to 2012 passenger levels.
Yes different areas would see different levels of impact, but even a 30% fall in many South East rail services heading towards London in the morning peak isn't going to leave those trains empty of passengers.
Yes travel patterns will change, but there's going to be some who will wish to carry on working in an office full time or nearly full time, including those in 1:3 goals which only have 1 person in (whilst quite a few are likely to be older people there's often a lot of house shares where they don't want to be with their house mates 24/7 and so would probably feel similarly).
There's other reasons we people would like to go to the office, including not having children distracting them (even if that's only after school and maybe even then maybe even only on some days).
The likelihood of WFH being an average of much more than 50% of time and it being much higher than 70% of all jobs being suitable (often 40% and 50% get cited, but given that rail is likely to attract more commuting from those jobs which can be done remotely I've used a higher figure), then there's 65% of rail travel is commuting. 70% of 65 is 45.5, 50% of that is 22.75, under that outcome that's a 23% drop in rail use.
However if 25% of people are working in the office full time, to get to an average of 50% then the rest would need to work from home an average of approaching 70%, that's 3 days a fortnight in the office as an average.
Most people wouldn't want to be in for less than 4 days a fortnight (2 days a week), but there's going to be many who would be fairly happy at 2 days a week at home. As such I suspect 50% average WFH is unlikely, and why a fall of 10%-15% is where I suspect that trail travel could up at once there's a bit more normality.