The majority of people cannot afford their own home at today's prices. That is the simplest metric I've found for the intergenerational robbery taking place.
The government will try their best to keep housing pegged but it will blow the gaskets off commodities and the cost of living.
Assuming OP means, "The government will try their best to keep house price increasing" although I'm aware that the use of the word pegged is confusing.
A common opinion is that governments feel that increasing house prices will keep the voters coming in as people work their butts off to get onto the housing ladder (escalator) and then want the bubble to keep expanding as it's their main form of savings. Western society is all in on the Ponzi scheme here.
I've heard it's less about voters directly, and more about the retirement savings being tied up in real estate so deeply that breaking the housing market would not only cost you votes, but probably turn the country into a humanitarian crisis.
We shouldn't forget the role of the financial industry in this. There's been an enormous wealth grab by the financial sector in the past 50 years or so. Those buildings in the City and Canary Wharf don't pay for themselves. They come from the money they hold back every time house prices rise.
The government will try their best to keep housing pegged but it will blow the gaskets off commodities and the cost of living.