Cause a tax amount that goes up based on what people with more money than you do on other pieces of property simply gives more power to the wealthy. "Underutilized" as far as tax implications go then means "people with more money than you would like there to be something else there."
And, of course, this already happens with US property taxes in many jurisdictions. And people absolutely hate it.
"Tax incentives to downgrade to a smaller property" sounds great in theory for retirees sitting in huge properties, but I think is limited in practice. The people with the really big places are wealthy and politically influential, so you'll get Prop 13s, or you'll get the recent cuts to property tax in Texas. "Make housing more affordable by cutting the taxes!" And the people impacted by more aggressive taxes will less be the boomers in giant houses and more be the poorer retirees in multi-generational living situations, or ones in fairly small condos.