Housing behaves just like any other good, in that as you learn in Econ 101, if demand goes up for something, only one of two things can happen: either supply goes up to meet that demand, or price goes up if supply isn't added. This is why (and I realize there are many more nuances and complexities in play here, but bear with me) any solution to gentrification must necessarily include allowing more units to be built to relieve upward price pressure on housing in a particular area.
Again, I am aware that there are other dynamics in play when it comes to addressing a lower-house-value area starting to rise in value, and therefore the need for other solutions besides just "add supply." But neither can one remedy the problems wrought by gentrification and displacement without including some "add supply" in the mix.
But the issues facing Silicon Valley are of a different sort, which is that of addressing hyper-unaffordability in a higher-house-value area. Here existing homeowners have applied sufficient political pressure on their local elected officials to oppose new developments on the grounds of environment, traffic, or aesthetics. But fundamentally, it is about self-preservation of one's house value. Here are two quite brazen quotes from recent articles that articulate what most people think but may be unwilling to say:
“Taking away two fantastic neighborhood schools to bring in low income housing is absolutely ridiculous … This would devalue home prices in the area significantly. This isn’t really a consideration, is it?”