Counting out rhythms is something that can only be done at slow tempos.
When tempos get fast and someone is trying to read notation, it is exactly like reading aloud in a native language - it has to be visual recognition followed by execution.
Basically, counting things out is how rhythm patterns are learned, studied and figured out (if there’s a problem) but when things get fast, the rhythm patterns have to be visually memorized so that they can be played accurately.
The method of slowly counting things out and memorizing the music or using your ear is absolutely fine.