Dunno where you were buying your hardpoints but the ones I've always bought had set on the teeth.
Only ones that were a problem were some £3.99 ones from Wickes.
I'd been buying the £3.99 ones for a while (they used to say Jack on the blade) then they changed them (no longer said Jack on the blade) and the new one had very little set. At the time I was working on a very big roof and was cutting a lot of wet wood so it was a problem.
Went back to paying a fiver a pop for the Spear & Jackson ones instead. No more problems.
I did a quick straw poll of types of hardpoints at work the other day nd there was Spear & Jackson Bahco 244 an Irwin thing and a Old style Wikes £3.99 saw.
Every single one of them had the same type of set. It wasn't alternate set, more of a skipset tooth pattern I would say.
Looking at the teeth it goes, left set, right set, no set, then back to the start as left set, right set.
I didn't have a micrometer to check how much set there was but I'll get round to it eventually.