Here in the UK, there used to be training that anyone could take that was offered by the main first aid organisations, lasted 2-4 days, and covered significantly more serious but not necessarily life-threatening conditions. There were a few variations you could do, including things like common sports injuries, conditions you might encounter while in the wild outdoors and how to handle a situation as well as possible if professional help is going to take a long time to arrive, variations on first aid for children and babies, and so on.
Those courses for the general public seem to have all but disappeared now, presumably due to a lack of demand. This isn’t entirely surprising, as they weren’t cheap to do, but if you did have the means to afford it, what is the value of knowing how to help someone recover better from an injury, or preventing a serious condition from maybe becoming a life-changing one, or in extreme cases even saving a life? My wife and I did take a course specifically on first aid for little ones when we were about to become parents, but even finding that wasn’t easy.
The main ways to get more than very basic first aid training here now seem to be through either statutory obligations for first aiders at work (where the courses are widely available and longer but also have to cover the official paperwork you need to do as a first aider at work) or through becoming a much more serious amateur first aider (either joining one of the first aid organisations and in due course going out to work as a volunteer at major events and the like, or through things like sports coaching organisations that have the scale to make special arrangements for first aid training). That leaves quite a large gap in provision for “ordinary” people who just want to know enough to help out in a serious situation, but as far as I’m aware, there isn’t really anybody trying to fill that gap at the moment. I did ask the trainers on that last course I took if there was anything I’d overlooked in terms of more comprehensive general first aid training, and they said that unfortunately the above is about right at the moment.
I don’t know how much first aid training would really help with the current coronavirus situation anyway. It seems like what is needed in this case is more people with nursing skills and the ability to set up equipment like ventilators. But as a more general point, I would strongly support measures to increase general knowledge of first aid within the population, at least for anyone who is willing and able to help when they can. If nothing else, it might free up more of the fully trained professionals to deal with the most serious situations and so help reduce the strain on them.
Just like a reserve army full of reservists has a serious cost (those people all have to spend weekends training, after all: time that could be spent doing other things), a "health care army" would require people to get regular training to stay up-to-date and in practice. Basic first aid can be useful for anyone, but for having people ready to jump in and become healthcare workers in a crisis, they need a lot more than a first aid refresher once a year I think.
If this goes really badly in the next couple of weeks or months, that's not going to be a true assumption. A changed nation is going to be looking at its spending priorities and a lot of reassessing will be done. Predicting exactly what the result will be is difficult, but predicting that there could be a lot of change is not.
If we cross the logistic curve's inflection point today, then this may ultimately blow over and be remembered as an inconvenience (and, humans being humans, an overreaction). If this continues on for much longer and kills hundreds of thousands and (based on some of the nasty stuff I've read about) permanently damages the lungs of millions more or other such things, causing disability and long-tail mortality increases for the next 50 years, this will be a generation-defining event comparable to the Great Depression, and the usually-reliable "tomorrow will be mostly like today" prediction methodology will catastrophically break down in the next couple of months.
Snark aside, we had a similar situation with SARS. In the immediate aftermath, it's easy to say what needs to be done to prevent the next one. It's far harder to get everyone onboard with paying for something 5 or 10 years down the line when "there's no point" and "why do I have to pay taxes"?
I'm happy I don't live in The USA right now. Even the worst hits, I don't have to be afraid of medical bills or if I lost my job. Both are covered by the tax I payed before.