I'm glad to see folks sharing about this topic and wanted to contribute my experience with everyone's application when performing at the drum kit.
For me, it was eventually adapting the "hand to hand" combinations of "musical rudiments" so that no matter what hand begins a pattern on whatever surface, the rhythm pattern will remain true within the time signature and meter of the piece.
Now I admit, that was easier 'said' by me than accomplished over the course of my experience and loving music.Perhaps the most significant recommendation given to me back in the mid 60s (when I actually started playing the drum kit) was by my teacher Morris Goldenberg - who recommended George Lawrence's "Stick Control." Then Billy Cobham himself recommended the same manual to me when I met him in NYC (1971). That was an "eye opener" for me, and for anyone witnessing Billy Cobham play live! I was astounded, to say the least!
Yet to the point, it was then when the Light Came On in my mind. I began to seriously embrace the fluid motion when "hand to hand" attitude is executed. And eventually, it didn't matter what genre of music was to be performed - although we all have our preferences about musical styles. That's an individual's prerogative, and I respect that. For me, I like Rock as much as I do Blues. I love ballads as much as I do fusion. I guess I'm just "mixed up" that way and eclectic! I figure I'm sane with the embracing!
Fundamentally however, I'm a right handed drummer. The challenge for me is to adapt the fluid sticking with "hand to hand" to any rythmic patter withing a song to be performed. The same applies to my feet when mixing up the "notes" with appropriate accents (usually given by either horns or vocals - and most certainly where the drummer finds himself within the musical phrase toward the "one!"). It's like when people speak with each other in a conversation: just listen to who's speaking to you and understand the context (genre): that's difficult to do at times because some anticipate too quickly what you are saying before it's understood. The same with music - think in terms of the musical sentence without fear of being cut off in mid sentence...
That's my attitude and hopefully one of many signatures among so many JAZZTASTIC musicians, artists and people in this World. You've ALL contributed to my life and I thank you - especially to Billy Cobham for his unique musical ear to the technicalities while bringing out distinct punctuations toward the period (punctuating The ONE in a musical phrase, sentence, paragraph and Piece!).