There have been attempts at such service in the past.
The Route 128 Business Council, which runs very successful shuttle services in Waltham, Lexington, and Needham, did try running a service from Anderson Station to Woburn, Lexington, and Burlington for about a year in 2005-2006
https://web.archive.org/web/20050723234848/http://www.128bc.org/wob-burl-lex/index.htm
Although the service was originally supposed to run for three years with grant money, it was discontinued after one year because of low ridership.
The City of Peabody ran their own mini-bus shuttle between Salem Station-Peabody Sq.-North Shore Mall-Centennial Park for over fifteen years from 1993 to 2009, but finally gave it up because of low ridership and high costs.
That's indicative of the problem. Not enough stakeholders with eyes on a long-term investment.
Peabody shouldn't have to go it alone trying to solve its transit deficit. All it takes is one economic hit like the 2008 crash and that's the end of that. And they can't get mindshare from commuters inside 128 with a purely municipal service.
One-and-done is also no way to grow ridership. Anderson was only 4 years old when they did that shuttle experiment. Between the '05 and '12 Blue Books its daily commuter rail boardings have increased 55%. But 128BC doesn't have the resources to run a loss leader for a few years while it builds momentum and they toil trying to line up more sponsors.
None of these DIY services are/were Charlie-integrated, which is a big blocker for reverse-commuters and for widespread employee availability to pre-tax transit subsidies. These are in-district towns so there are no Regional Transit Authorities with state-level coordination available to step in here like they do on some of the trans-495 stops. It's outside the jurisdiction of the LMA shuttles. Massport isn't in the business of providing radial transit. The T has to run some real routes out here. Or...there needs to be a public half of a public-private partnership outfitting the 128BC shuttles with Charlie integration to boost the transfers and access to universal employer subsidies, and offer some operating subsidy to backstop a fledgling service while it takes root and encourage schedule expansion. It simply ain't gonna happen any other way.
Anderson and Salem + Beverly have the heaviest commuter rail schedules of any individual stops on the system: 27-31 inbounds per day, 27-29 outbounds per day. Slightly better than Westwood/128 and hands-down better than any other station. Commuter rail frequencies are just fine for supporting robust connections. The only thing that needs to be squared is the Zone inequity that unduly punishes the North Shore: Anderson, Reading/Wakefield, Dedham Corporate, Westwood, and all Needham and Waltham stops are Zone 2 while Salem's a 3 and Beverly's a 4.
Other than that all you need are buses: locally-originating and CR-coordinated schedules, meaningful enough quantity of schedule slots, fare compatibility, commitment to see it through to slow growth instead of pulling the plug the second there's a funding blip, adequate promotion, and robust outreach to the private stakeholders. That's not going to happen on the Yellow Line until the T breaks out of this holding pattern of keeping service levels flat and thinning services in one part of the district to preserve it in another part. The outsourced carriers can't do it alone or commit to building it from scratch to the long haul alone. These areas just aren't going to get the access without some state involvement at seeding the ridership.
And I don't see how the commuter rail's growth cap lifts to support more off-peak service or DMU's beyond Zone 1A that touch all the way to 128 unless the riders can get somewhere beyond the station parking lot or a few blocks of immediate downtown environs. Those conditions don't ripen at all without a concerted effort at circumferential buses and reverse commute options. Arguably the bus route seeding needs to immediately precede the off-peak train expansion if any of these stops are to pay back some of the higher operating costs.