Why doesn't cellular, replicative senescence (or the hayflick limit) constrain the normal development of an organism?
You pretty much have answered your own question. It is a math problem. Cells are burning up their telomeres during fetal development onward but the cells are multiplying exponentially in number. 

But biology is a bit messy, embryonic stem cells do have telomerase activity and their telomerase are maintain. So the clock doesn't start counting down immediately.  https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2360127/

Temporal wise hES cells are around 4–5 days post fertilization, at which time they consist of 50–150 cells. https://en.wikipedia.org/wiki/Embryonic_stem_cell. 

So you don't quite start with an n of 1 cell. But of an n of 50-150 (in humans)... before you start to see telomere shortening. With that head start those 50 doubling can make a lot more cells. By my guestimate with excel ~1.69E17 cells ~320 tons. More than enough you to last a life time.)