Even though r/t EGT is much lower and for shorter duration than TO & climb, it is still an additional thermal cycle on the engine, therefore a quantifiable cost element. Cheaper than brakes? I'll leave that to someone else to determine.
I concur with FullWings about FOD risk too - not just the massive or obvious FOD, but the more subtle erosive kind that comes from sand or wintertime runway treatment.
But deploying idle reverse early after touchdown is relatively cheap insurance in that it can save a few precious seconds when needed.