Sub-area equity and ridership analysis are used to counter this, hence Seattle building its light rail network through one of the poorest & highest transit ridership parts of town, and continuing it north through U-District (where cheap studios can still be had) up to Northgate and eventually Everett.
Would be gentrifiers are in for a rude awakening: http://theneedling.com/2019/08/12/thousands-of-engineers-fle...
I thought one of the major issues with light rail was how much it costs vs. just using buses? If a last-mile transport option is nice but very expensive then it'll only be installed in richer neighbourhoods and therefore largely be used by richer people.