Yes, A10 sounds much more exciting than another A3 or an A2. And really, it behaves like a core burner, it just has a wheezy sustain phase once the grain transitions to end burning. In order to make a BP booster motor you need a bulkhead of BP to prevent staging midway through the burn and the result of course is a low thrust sustain period due to the larger nozzle needed for hte boost phase. In the end - "who cares?"
Re your second paragraph - average thrust is important, and choosing between one and another I'd still say average is smart. But in many cases you must look carefully at the thrust profile of the motor if there is a concern about a particular phase of the flight. Similar issues can be observed in various HPR motors now and again - where for example one may decide not to use a particular motor for a particular rocket due to the average thrust not satisfying a rule of thumb such as 3x GTOW, yet, because the motor has a notably regressive thrust profile it may be a perfectly acceptable choice. Tangent port (moon/C slot) motors are one example that comes to mind, as well there a few fairly regressive core burners as well either due to grain L/D or nozzle erosion. Although you may make a very educated choice to use a particular motor that you know will have good performance off the pad, you still have to convince the range safety officers on the subject - that may or may not be a challenge.
Where rules of thumb can bite you is with progressive thrust motors, in rockets where you are marginal with liftoff acceleration based on AVERAGE thrust to begin with. Though I think it is true to say that progressive motors are the minority these days.When erring on the side of caution, generally those rules of thumb work quite well. When on the edge, take a hard look at the performance in the early phases of the motor burn.
Mike D.
p.s. enough on mini motors.. ;-)