I can understand why anti-gentrification advocates might want to increase the height limit - denser downtown development means less displacement on the downtown fringes. Of course, right now such people hate developers, so they won't do anything that might help their sworn enemy.
I can also understand why developers might want to increase the height limit - bigger projects are more efficient to build, it would enable cheaper design features like above-ground parking podiums and allow them to make more money with less land.
Right now it seems like these two powerful forces are sort of in a stalemate that keeps the height limit untouched and preserves the status quo of an expanding downtown.
But from a planner's perspective - isn't the height limit working exactly as intended? New development is spread over a pretty large area. More and more parts of the city are becoming dense and walkable. Developers are building neighborhood-scale projects that often integrate new public space and even (minor) transit improvements, so it takes some of the burden off of government to provide these things. The only planning argument against this is that the city is now struggling to provide full-fledged transit to these newly developed areas. However, even with more intensity in the core, WMATA would still be struggling with severe capacity issues at places like Metro Center and Farragut. Arguably, their current plan of building a streetcar network to serve the downtown fringe is much cheaper than expanding subway stations and building whole new relief lines...