My suggestions to improve would be better funding for light rail, dedicated lanes for buses that other vehicles can’t enter, priority access at intersections, and a congestion charge to enter the core (“The Loop”).
EDIT: Dropped "light" from "light rail system".
While I'm less well versed in the governance issues of the MTA, it seems as though control should be passed back to local voters, as the NYC subway has been dealing with a fair amount of issues as of late also, and it appears the governor and mayor can't agree on who's fault it is and who should fix it.
We see a gross form of state's forming supra-state policy in the National Popular Vote Interstate Compact, but with NPVIC each state is working on it's own to pass the compact, each state it's own independent stakeholder, whereas if you want to get DC, MD, and VA and other local regionals voting to fix WMATA, I believe there needs to be some supra-democratic structure the states can form.
It hasn't broken down too many times, and is reliable enough that many New Yorkers don't own a car (which IMHO is the gold standard for trust in a public transit system).