Is the pull start on most 4 stroke kits a weak point?

Another reason you see broken pull starters on a 4stroke engine, is the bike falls over & breaks the plastic pull start housing.

It unexpectedly has happen to me on my huasheng 142f cruiser bike.

I've also had them fall over & bend the metal pull start housings as well.

Soo Stuff Happens!
Sidewinder said it, gently pull it around until the compression stroke and give it a short pull after taking up the slack with the starter engaged in it's dogs.
Have you ever tried to start and old Stihl chainsaw that just refuses to start. Pull and pull and pull, just won't go. If you use the rope and and just turn it over a couple, three times, and then try to start it, it will go. My buddies saw is like that, he'd prime the carb to get it to start. Then I showed him how to just rotate the engine a few times before giving a good yank.