The issue is whether or not a breaker is required to simultaneously open both poles on trip when serving only a line to line load. It is not required when serving an three wire single phase MWBC. That case only requires that a manual opening affect all poles.
. . . that supplies only L-N loads. If there is a mix of L-L and L-N loads on the MWBC, then common trip is required.
I think a reason common trip is required for a mix of L-L and L-N loads on a MWBC is that current could still flow between L-L and L-N loads that are connected to the same phase if the line supplying that phase is opened by a breaker but the other line(s) of the L-L loads are still hot.
I'm curious about 240.15(B)(3), in the context of a 3-phase system does the phrase "line-to-line loads" imply single phase 2-wire loads, or does it also include 3-wire delta connected loads?
Good question. It could also be asked whether "open delta" loads between two pairs of phases would be included in 240.15(B)(3).
To consider this let's take an example where there's a 12
Ω load between lines L
A and L
B, and another 12Ω between L
B and L
C in a 120/208 3-phase system. Then the current through L
A and L
C will be 208V / 12Ω =17.3A. The current through L
B will be 1.732 x 17.3A = 30.0A. Now if there was an individual 20A breaker on each phase, the breaker for L
B would blow from the overload but those on L
A and L
C would not. Then the two 12 loads would now be in series across L
A and L
C with 208V applied, and so they would still be drawing current (half of their previous current or 17.3 /2 = 8.65A).
I think this simple example shows that an individual single-pole breaker feeding L-L loads connected to more than one other phase would not fully interrupt the current through those loads. So in that case I think a common trip would be needed for the same reason mentioned above for not allowing individual breakers with a mix of L-L and L-N loads on a MWBC. I think 240.15(B)(3) should be more explicit about this if that was the intent.