This does happen on Amtrak, BTW, with the separate halves of the Lake Shore Limited. With a practice instituted entirely within the modern era--1975--since the LSL never existed in the private RR era at any rough facsimile to the way it operates now. Boston section pulls in headed by a diesel and usually carrying the cafe car for use by everyone Albany-Chicago. New York section pulls in headed by a dual-mode and usually carrying the dining car for use by everyone Albany-Chicago. Dual-mode locomotive
separates off and heads to the yard, Boston consist maneuvers in and couples. The opposite happens on the trip home.
But that's waaaaaaay different with coach trailers than it is with MU's. A coach only has a 'dumb' connection of straight electricity for the lights/HVAC/wall outlets and a very simple pass-thru data connection for the PA/door controls/emergency telecoms/etc. Trailers not only don't fault often, but when they do the crew can just do what they do on commuter rail and run a single car in the dark or move passengers to a different car and isolate it. The Lake Shore Limited doesn't even run push-pull--it's pull-only with no cab car--so it doesn't even risk the most common kind of commuter rail car fault: wonky connection to the cab car's controls when changing ends. Amtrak also has the added advantage of its big Empire Division home yard being 200 paces in eyesight of the A-R platforms and having large onsite staff of maint techs, plus rescue trainsets onhand if the LSL has a problem and everyone needs to change trains. They wouldn't risk splitting that train at all if it had to run with a cab car and didn't have a big maintenance HQ right there.
Any MU's, including subway cars and trolleys, have much more complex data connections. Multiple units have 2-way communication between all cars for balancing out individual cars' propulsion, so an unnsecured cable from a bad coupling is going to cause faults galore and leave a train dead in the water. That's what gets every operator risk-averse to doing it at all unless there's zero alternative (like Matthew's MUNI example). Bang trainsets together in the field enough times and the connections start to wear out. We see that all the time on the Green Line, where trainsets get split up and recombined in the yard more often any other mode in Boston. The Type 7's that have yet to go through midlife overhaul are glitchy as hell, with the 'reboot' epidemic being the end result of worn-out connectors causing MU'ing faults. Oldest Red and Orange cars also fault enough that they take great pains to keep trainsets together as much as humanly possible. As do some of Metro North's and NJ Transit's most ancient EMU's. It's one thing to have gradual wear-and-tear causing faults in the yard, and another at a station stop with passengers onboard...miles from a maintenance base under time crunch to keep schedule. The extra overhead it takes onsite to be fail-safe just ends up lathering on too much extra cost and OTP penalty. So nobody, including the first-worlders, does it except in those very limited no-alternative scenarios.
Certainly nobody dreams up
new installations of split-and-combine ops if they can avoid it. And here at least there's always a crying need to backstop mainline frequencies with extra trains--even if they're expresses--so doing something branch-centric passes up too many easy-grab extra frequencies to ever be worth a consideration.
For this Auburndale example, one of the things Indigo accomplishes is cleaning up the increasing glut of inside-128 stops that bog down the Worcester schedule and over-fills the trains. Worcester's schedule could improve a lot if it didn't have to serve Newton and Allston once every couple of trips to feed those stops with some baseline of service. They aren't MetroWest or past-495 reverse commute destinations. So I could see in an Indigo world 80% or more of Worcester-proper trains skipping Auburndale-Yawkey entirely for sake of keeping the Worcester trip closer to an hour. And then Framingham locals consolidating Newton to just Newton Corner with its superior bus connections, and a pick-'em of 1 or 2 of the Yawkey-West-New Balance trio--perhaps a rotating cast in different schedule slots--to give Allston and the campuses baseline representation. Then let Indigo handle the whole inside-128 string exclusively.
Extra mainline frequencies accomplishing the service goals for each distinct audience and each distinct audience's demand profile: inside-128, MetroWest, past-495...and where each of those groups of commuters need to go in the largest numbers at the most tolerable travel times. Not a situation where uncoupling accomplishes anything because it drags down an outside-128 schedule that badly needs some semi-expressing to keep good time.
Survey any current or potential commuter rail line in all 6 New England states and you'll find the same thing: the extra mainline frequencies are just too valuable to pass up when you've got an opportunity to grab extra slots or balance the needs of different audiences that traverse the mainline. I actually can't think of any applications on the whole Eastern seaboard where splitting even asks the right demand questions. Maybe somewhere in the Midwest or Mountain West there's a fit, but it's pretty cut-and-dried what the needs are East Coast
and West Coast whether we're running a first-world Euro style network or just more of the same.