but the important thing to keep in mind is that high fees damage and eventually prevent adoption. example is Steam (Valve), Reddit,... stopped accepting bitcoin payments. so although in short term high fees may not prevent bull run (this bull run for instance) but in the long run if things remain this way there will be no more bull runs anymore because bitcoin will be unusable and may even be replaced.
what do you mean "bitcoin's role in it"? there is only one bull run and bitcoin price rise is IT. there is nothing else!