We were ready to drop 20% on the house because like you I was also scared of PMI but when we ran the numbers with the bank the cost was small enough that it didn't make one iota of difference in the long run so we paid 5% down and have a very flush emergency fund.

Someone with good credit and currently renting would be nuts to "wait and save" for even 1 year because the total cost of PMI was like 6mo of our rent and accounting for paying it off over time with inflation it's probably even less than that in real dollars.

Maybe we got lucky with PMI but googling a bit it doesn't seem that out of line with the calculators.