Currently It's like a cabinet post - the best person for those jobs is always going to depend on the governor's preferences, and the job description changes every time someone is in the top seat. Structurally, I'd suggest taking the hiring a GM role away from the Governor/MassDOT secretary directly, and assigning that role to the MBTA Board - much in the same way a corporation's board is responsible for their CEO. That would reduce the political effect on the GM role, in so much as the governor is limited to influencing the board, like a majority shareholder.
Frankly, I think the driving thing behind Eng's competence is operational experience leading a major transit organization, and I think the way to keep the T run competently in the medium term is for Eng to build a deep bench of operational talent in the middle upper ranks for future govs to draw from, and who will be in post doing the meat of the work. At least part of this is that senior executives qualified to run a major transit agency are in relatively short supply. There's what, roughly a dozen North American transit agencies with the depth and breadth of the T? External talent like Eng and the team he brought up from NYC won't necessarily be available when the T needs it. NYC took Rich Davey... it's a finite pool.
Look at the last 5 GMs - of them the most recent 3, Poftak, Ramirez, & Shortsleeve - none of them had transit experience before the T. They’re all management types, more comfortable with boardrooms and cost accounting than trains. We got Eng from the LIRR, but before them, Beverly Scott came from MARTA, and seems to have been generally competent before the 2015 snowpocolypse - but even that was nearly a force-majure incident. Following was DePaola, a 20 year T engineer who, by all accounts, kept the T running during that winter before he retired with cancer. The job needs someone who has that depth of experience to draw from, and then look at the T's leadership when Poftak resigned. Who at the T, in a AGM or Chief officer would have been qualified to take over?
Bar the DGM Jeff Gonneville, (who appears to have recently resigned in May) the bench was woefully bare of anyone with real operational experience, being mostly MBA types. Eng is building the bench, with new "Chiefs of" that actually have operational experience running the system like Ryan Colohan as COO - and by the podcast episode he was on, that's currently a focus up and down to build an internal talent pool, from maintainers to management. That's where I hope the next generation of T leadership comes from.