10 years ago or more roofing felt was made differently than it is today.
Back then a good felt job would hold up for at least 2 weeks and likely twice that.
The felt of that time was thicker and had more asphalt saturated into it, many affixed it with staples and some used cap nails.
Nowadays most felt is complete garbage even the 30#.
When exposed to the sun the stuff shrinks and pulls away from the staples so now it’s not affixed very well anymore and there are holes in it.
This only takes a couple days.
Most of the felt made today doesn’t meet the D226 standard that felt is supposed to meet to be suitable for rooftop use.
The last time I used a Premium 15# (Certainteed roofer select) felt it rained for 2 days and the crap got saturated and water went right through it, it was on a new build but it still made me look bad.
I’m sure there is still good felt made but it is not available to me unless I special order it a pallet at a time.
I have had many houses facing West on lake Michigan felted in for a month or more hold up to wind & rain with just felt and no leaks in the past so it’s not that felt is not good.
The synthetics cost 3x-5x as much as felt when the cost of the cap nails is factored in, so synthetic is far from inexpensive for what it does.
If the building is going to be shingled the same day it doesn’t matter at all which underlayment is used and in fact felt is better because it breaths while most synthetics do not.
For a long term temporary roof type dry in the synthetics can’t be beat, they need to be properly affixed with the right fasteners though.
There are a lot of people that affix the synthetic with standard staples, this negates any advantages of using synthetic in the first place but if shingled the same day does not matter at all.