I think establishing a foundation of addition and subtraction takes far longer for children to master than you're considering, especially since there is evidence that children of this age appear to intuitively view numbers logarithmically rather than linearly [0].
I suppose you could take advantage of this by somehow prioritizing multiplication and division over addition and subtraction, but I think there's too much value in comprehension of linear numbers and addition/subtraction since that is the lion's share of interactions they will experience at that age.
On the other hand, if you're merely talking about abstracting multiplication and division into patterns, then I wholeheartedly agree with you, and there is evidence supporting this [1]. Although pattern identification is already part of kindergarten/1st grade curriculum here.
Ultimately, IMO the most important aspect of education in general is covered in the open letter linked to the OP:
> There cannot be a “one size fits all” approach to K-12 mathematical education.
My children have thrived with their current math curriculum, and I know some of their classmates have struggled in contrast. One size does not fit all in education, nor in many aspects of life.
0: https://news.mit.edu/2012/thinking-logarithmically-1005 1: https://www.tandfonline.com/doi/abs/10.1080/15248372.2012.68...
But don't ask me about division, my siblings/parents/whoever tried to explain it as "the opposite of multiplication", which was complete nonsensical gibberish and I didn't learn division until years later.
So I'm not saying it can't be done by any 5 year olds, but it seems young to teach this to the majority of 5 year olds.
Though empirically, I don't know about age 4 but kindergarten is definitely not too young for learning up to 12*12. And once you figure out multiplication and eventually mental division, it's not too big of a leap to have one variable algebra with "move a plus to the other side to become minus" etc. The formalism can come later but it's fantastic to have some exposure to moving numbers and symbols around from an early age.