Road wont suffer for any such reasons- if anything this has shown how essential car and road usage is to people’s lives and the economy - both to the people and decision makers.
Road will suffer because the projects are smaller and easier to cancel. Especially as so many are in the future.
HS2 has nothing really to do with rail investment as your post makes clear - we spend a fortune already. Already marginal cost benefit wise and politicised, it’s future depends on the impact of cancelling it and just how bad the govts general figures are.
Again, just as roads it could be deferred, even at total overall cost - look how “prudent” Brown near doubled the cost of the aircraft carriers.
Tax wise I doubt there will be very much - with so many having lost significant income, and that affecting all brackets - there will be zero appetite to pay more tax.
Cuts seem far more likely, everyone wants more NHS but this might focus minds on what that means, and I believe when given a choice, as politically it will be, people will choose their own pocket. No doubt there will be stories galore of how consultants and overtime payments meant some profitted, and the supply side too - harsh but it’ll happen.
Covid-19 & WFH is likely to have an impact on road usage for the next 5 years, given that 10% of all road traffic is directly related to schools then a drop of that much would allow the cancelling of probably the next 5 years of road projects.
There's two factors which will likely impact road use. Firstly the lockdown will force a LOT of people to try delivery/online for a lot more goods and services than they would have been willing to accept in the past. This will reduce the "need" for cars for a lot of shopping purposes. Combine that with the potential for shops to close some of their branches (almost certainly where there's more than one in a town or urban area) and redeploying those resources to delivery.
That is likely to have an impact on the viability of town centres and or retail parks. Which in turn is likely to impact on coffee drive thrus (especially combined with that people will have likely got used to more normal coffee, if not reduced their dependency, during lockdown).
Secondly WFH is likely to increase for many. Not least due to the fact that businesses have realised that even though they've taken a productivity hit they could cut their lease costs by having smaller buildings.
For instance an company with 100 people with 50% working from home 2 days a week could have a building which is 20% smaller than is currently the case. Add in another 25% who work from home 3 days a week and the building can be 1/3 the size. That's likely to be quite a string driving factor, given that much of the IT infrastructure had already been deployed and stress tested.
That still shows you to have 25% Worthing in the office full time, which could include new starters until they've demonstrated their work ethic, those who have shown that they can't be trusted to work from home and those for whom working from home brings no advantages or creates challenges (such as there being small children around and no dedicated work space).
For those who do WFH then there's going to be questions over the cost benefits of car ownership.
At a very simple level of it costs you £200 per month in car ownership and running costs (£100/ month on fuel and tyres isn't that difficult to achieve, nor is £100 servicing, £200 insurance, £100 VED, £30 breakdown cover and £770 in purchase costs each year, with many paying a lot more than that) then on a 20 working day month that's £10 per day. If that falls to a 12 working day month (as the other 8 are all working days but just from home) then the cost jumps to nearly £17 a day. If train fares are £13 a day then there would have to be quite a bit of other use for that car to justify the extra cost. Whilst £3.75 a day doesn't sound a lot, over a year of 3 day week it's an extra £540. That's at least 18 days of car hire at £30/day, which would probably cover most trips you wanted to make.
However the maths gets even worse of you're a could and you're both working from home two days a week and you can mostly do so on different days to reach other with the one going to the office mostly being able to drive and only 1 day a week where you regularly have to have one person use the train. As then the cost of running two cars over one would be very hard to justify.
Given that to get a 10% fall in road usage we'd need just 15% of all road users to WFH 2 days a week then that's relatively easy to achieve. In reality it would need to be less than that as people significantly reduce the above of face to face meetings they do. Even if you only did so for 1 meeting out of 4 that's going to have an impact on the overall traffic flows. Which in turn reduces the numbers needing to work from home to achieve the 10% drop in traffic.
However even then there's likely to be a bigger drop in peak hour traffic with people looking to do longer hours working from home (say you've got a 30 minute drive to work, those days you work from home you do a +1 hour working day) so that you can then work shorter days when in the office (maybe arriving at 10am) so as to shift your drive away from when the roads are at their busiest.