I am pretty sure the escape analysis doesn't affect the initial stack size. Escape analysis does determine where an allocation lives. So if your allocation is lower then what escape analysis considers heap and bigger then the initial stack size, the stack needs to grow.
What I am certain about, is that I have runtime.newstack calls accounting for +20% of my benchmark times (go testing). My code is quite shallow (3-4 calls deep) and anything of size should be on the heap (global/preallocated) and the code has zero allocations. I don't use goroutines either, it might me I still make a mistake or it's the overhead from the testing benchmark. But this obviously doesn't seem to be anything super unusual.