What they did in the 'olden days' was not do half the tests we now have available, tbh. 
I'm sure, if it really comes to it, there'll be a switch to whatever there can be, but it's debatable how much of the 'traditional' equipment is still around and available, how many people are trained to use it, and whether the labs can even process and analyse samples drawn that way.
It's such a simple thing but it has the potential to be catastrophic. We're used to being able to have all the data we get from blood draws, used to relying on it for diagnostic guides and warning signs, used to being able to 'rule out' things by throwing a blood test at it. It's a relatively quick, cheap, non-invasive tool.
It's crap for patient's, but I feel genuinely sorry for the doctors and nurses, too. They don't need their working conditions made any harder right now and this could be a nightmare for them.