All of this - buy-to-let, buy-for-not-let, empty homes is totally irrelevant. If houses are available to be bought as an investment then some people will buy them as an alternative to a pension fund, savings etc.
This is the private sector - what is needed is more social housing and talk of compulsory purchase of people's property is just hot air - it is like saying that someone has saved too much in investment funds, the bank, whatever, for their retirement - let's take it off them and give it to the poor.
What is needed is more decent social housing at affordable rents - if there was sufficient then people owning buy-to-let whether renting them out or not may perhaps then sell and first-time buyers would have more houses available to purchase at a reasonable price.