It seems from my naive perspective that Google and/or Microsoft could modify their existing workspace products quite easily to make then suitable for use in hospitals, no?
No. This is a very complicated domain due to the stringent legal requirements (which vary by country of course). Also, going in to healthcare software would trigger anti-trust lawsuits in a number of regions.
Google will sign a BAA and can be used for PHI, I'm sure Microsoft will, too. Not sure what you mean here.