All good answers.
I think
@toddbishop has the correct framing in that being able to lead with alternate hands is more or less the more important goal.
For me this is how I look at it.
In school we had to learn the rudiments, there was 26 we didn't go into the hybrids, this was late 90s-early 2000s.
Now, I am not sure how many PAS has now, but the material is out there if you would like to work on those sticking patterns.
When I worked at the music store, I would peruse the marching and theory sheet music for percussion, and work on them during slow periods.
I even jotted down some of the more memorable and have a few scratches of that available today.
After a few years of extending my rudimentary experience and learning some hybrids, it dawned on me that:
Rudiments are akin to driving along the road, you may need to switch lanes, avoid hazards and obstacles, and to get into better position for a pass, or maybe a sudden turn or stop that you can't completely come to in relation to traffic flow at the time - so you break accordingly, shift down or up to obtain the correct gear correlating to your speed.
If you break and shift all the way down, you're going to have to catch up, potentially distressing the environment - same in the music sense.
If you watch all the signs, and note the scape, you take the proper signals (or rudiments) your exchanges are more flowing, and your next rudimentary move(s) present more 'exit' options rather than a building catch-up-to-speed from gears neutral, first to whatever.
I guess you could use it in boxing as well, you don't just alternate jabs or haymakers, you are tactically setting up an opponent for the most effective opportunity without disrupting
your sense and balance.
Sorry I know that was hard to follow, I hope you get the jist.
I am pretty good with my left and right hand's dexterity, as I go through life using both sides for different functions.
But saying this, I need to work on stick dynamics or control, for some reason, the stick strokes pitch (7A) sound different hitting the same head, even when I switch the sticks over.
I am not a flailer and my stick height is on the rigid low side (think concert and marching), I am thinking grip (as I do have a different hold left and right) or some other micro kinetics.
Maybe some recording or mirror time would help me with this.
My left foot is catching up, I can feel me using left foot lead or back beat left double bounce rather than alternate stroke foot patterns.
This is starting to be more natural as I am exploring ways to use it effectively.
It does take time and like most, practice using memory, books, or rudimentary exercises, just do it with both hands for dexterity's sake.
Your brain will catch on to what your sticking idea is, just focus, and don't be like me but make sure the feel of dynamics and control are consistent on both hands and/or feet.