Generally, when the player draws aggro from an enemy, the music changes from normal to 'combat mode' and since this can happen without the player knowing it, it is essentially an early warning alarm to the player that they are about to be attacked. To me, this breaks immersion, and I'd much rather the combat music didn't warn me of an impending threat. My solution is that it should kick off only when the player actually takes damage from an enemy, thus eliminating the early warning effect.
This has actually forced me to remove the combat music from my data folder but then when things get quiet I still know what's coming. That is much less of a problem, but if I'm paying attention I can still anticipate an attack.