The physics, reaaaalllllllyyy, please, explain.
Let's start by quoting the (in this case 2006) Sprinter Owner's Manual (page 266): (emphasis added)
Do not loosen or remove the battery terminal
clamps while the engine is running or the key is in
the ignition lock as this could damage electrical or
electronic equipment beyond repair. All electrical
consumers must be switched off.
As for the physics, the battery is an energy storage device which also serves (as a mental model) as a capacitor ... voltage spikes elsewhere in the wiring are (very) effectively "eaten" (surpressed) by the battery... high voltages serve to charge it, drop-outs are fought by the battery supplying the "missing" voltage/current. The alternator really has to *work* to haul the battery voltage up to the 14.x charging level. Disconnecting the battery mid-flight very definitely removes that "capacitive" protection.
When you suddenly disconnect the battery, the alternator and any inductive load (wiper and fan motors, relay coils) will suffer a voltage drop (or rise, as soon as the alternator system notices and can respond to, the drop-out) .... that's called dV/dT (or dI/dT for currents) in electronics-speak. That rapid change is equivalent to what happens in a gasoline car's ignition coil: rapid disconnect (ignition points opening) creates a very short dT (in the denominator) hence very high resulting voltage or current (depending upon capacitance or inductance of the chunk of the circuit you're looking at).
Look at the relay choices MB uses throughout the Sprinter ... many (but not all) have resistors (or diodes) bridging their coils to *fight* ("snub") those dI/dT effects... without them the collapsing magnetic fields can generate voltages far in excess of "12v".
The alternator's coil is similar, and bigger ... although the regulator will *try* to control it, it does take a noticeable amount of *time* (from sensitive electronics' point of view) to react to sudden changes. (there's a reason a coil's inductance is also called "reluctance").
The Sprinter has many distributed sources of inductance more than happy to supply unwanted voltages, and damn few distributed capacitors to soak them up.
Disconnecting the battery while running is very definitely an "old school" technique (i used to do it to 1960s VWs and Porsches) ... but the fly-by-wire Sprinter ain't old school.
--dick