A government option doesn't mean that it's the only option. No one suggesting the government provide housing is suggesting that it becomes the only provider of housing. One of the primary goals is to ensure a good supply of at cost housing stock that can give renters some security and act as a controlling factor on private rents and house prices.

The UK sold off much of it's public housing stock after the 1980s. The scheme was billed as a way to get poor families onto the property ladder but many of the homes were "resold" the same day to private landlords. The result is that housing is now massively unaffordable except for the highest earners and landlords. Private landlords drive up buying prices to the point that individuals cannot afford the deposit because they can extract the cost of the mortgage + profit in rent, the higher rents then make it more difficult for the individual to save the required deposit and the cycle repeats.