To do this, I would:
1) Eliminate the current system of "unanimous consent," which allows each agency or municipality to hold the rest hostage on any issue or project, with no transparency or accountability to the public;
2) Reform membership to include NJ and CT counties in the metro area;
3) Promote transit/train agencies from advisory to voting members, on equal footing with the DOT's
4) Add NYC Parks as a member, as it is co-owner of many transportation facilities (parkways, greenways, waterfronts);
5) Weight representation to reflect populations, so that suburbs cannot dominate the city.
6) Reduce earmarks, which do an end run around the whole process!

Just changing the membership will not change the power, of course. City Planning is a member, for example, but is nothing but a cipher, giving NYC DOT an extra "vote". We need a mayor who instructs all city representatives to come to a consensus on what projects serve the full interests of the city, not just those of DOT.

Another problem is that these "companies" are all part of a regional agency anyway. Most of the buses run by the MTA Bus company are in Queens, but their headquarters are not located in Queens, and they don't do much outreach in Queens. For that matter, the Queens-based "private" bus companies that they took over weren't accountable to the people of Queens in any meaningful way. The only significant exception to this is Long Island Bus.

Another factor is that to the extent that, say, LIRR is responsive to Long Island residents and NJ Transit is responsive to New Jersey residents, it ignores that customers are not necessarily residents. I've had a job in New Jersey and been a regular passenger of NJ Transit, but as a Queens resident I had no say in any NJ Transit policies, even though I paid NJ taxes.

Unification would mean less duplication of administrative structures; there's a lot of management duties that could be shared among the various agencies. That would mean that people who are currently duplicating each others' functions could be reassigned to more important functions.

Regardless of unification, I agree with anonymous that better cooperation is essential. Not just in terms of cross-ticketing, but in schedule coordination and eventual progress towards through-running. One problem with framing this in terms of unification is that it leaves New Jersey out of the equation. It's hard to imagine NJ Transit operations ever being merged into the MTA, but the need for fare and schedule coordination between NJ Transit and the LIRR, or between NJ Transit and Metro-North, is as urgent as that between the LIRR and Metro-North.

First, the distances are too great. Where would the President of a combined LIRR/MetroNorth be located? And a regional bus agency?

Second, every time something is regionalized, more money is diverted from less well off people in NYC to better off people in the suburbs. EVERY TIME.

What we do need, though, is better integration of the various MTA (and not just MTA) agencies from a customer's viewpoint. Have through ticketing between the commuter lines, and between commuter lines and the subway. Just because two services aren't run by one agency, doesn't mean they can't cooperate. Look at the PATH train, which accepts Metrocards, despite not even being part of the MTA.