Should Left Handed Drummers Play Open Handed?

Left handed drummer: The most logic approach for a left handed drummer, in my mind anyway, is to set the drumset up for pure left hand drumming (the opposite of right-handed set up).

Since almost every drumbook and rudiment is made with right-handed drummers in mind, one can see every practice / rudiment start with the right hand. This then fit logically in with right-handed set up drumset. My advice to left-handed drummers will therefore be to practise drumbook / rudiment mirror-vice: Where the drumbook / rudiment says ‘r’ (right hand) the left-handed should play ‘l’ (left hand) and vice versa: When the drumbook says ‘l’ (left hand) the leftie should play ‘r’ (right hand). This will make the playing more logic (and more fun) on a drumset organized pure left-handed – mirrorvise of a right-handed setup).
This will also make playing 16-th-notes on the hi-hat with alternate sticking easier.
I am a very left-handed person. I started playing drumset with a right-hand approach, and did that for 14 years – ending up frustrated, as I felt something was not working the way I wanted it to do, especially regarding the hi-hat. I then changed to open-handed approach – and it felt much better. I was still however not satisfied, as open-handed set up did not allow for playing 16-th-beat with alternate (v-r-v-r-v-r-v-r) sticking. So I therefore turned the drumset completely around for pure left-handed playing. I also started to do all practise (book / rudiment) left-handed, as I started playing ‘l’ where the book / rudiment says ‘r’ and vice versa. I then also automatically start roll and rudiment with my left hand.
So now I am a much more happy (left-handed) drummer.