That's a fair question.
I've had what I consider to be an appalling run with KL from BRS, with planes being cancelled (usually because they've gone tech on arrival), or delayed and causing me to miss connections at AMS. Essentially, all the value of their service comes from reliability and punctuality, and my experience of both has been truly awful. I've also found them very wanting of customer service when things go wrong, probably because they have no dedicated staff at BRS.
My personal experience seems to be echoed by colleagues and other people who travel from the airport. In particular, people seem to have exceptionally low expectations of bags connecting at AMS. I gave up checking in luggage with KL when they lost my bags at AMS *in both directions* (on a two day trip!).
So my choice is to de-risk my travel (considerably) by not using KL, and by taking the hit on my time travelling to Heathrow. (Incidentally, I *never* had a problem with the FRA service).