That's the only time I use conventional is if I'm running it a very short amount of time to rinse out, because of fuel dilution or whatever reason.Been running synthetic in my Honda GCV160 lawnmower for 15 years. It still runs like a top and oil drains clean at the end of the season.
The "use conventional for break-in" talk is mostly because it is less expensive. Do multiple changes during initial break-in with inexpensive conventional oil to get the wear materials (glitter) flushed out. Then fill the crankcase with whatever you want for the regular oil change intervals.