Two factors likely come into play. First, the ignition system has all the battery power to itself for a stronger spark. Secondly, when you push start, the engine reaches a higher rpm than the starter will turn it. This is just my opinion but it makes sense to my old brain cells.
With the engine running in this very lean hot condition may cause all sorts of things like burnt/broken valves, a holed piston and the piston rings will also be damaged. You might even wind up seizing the engine. Sounds like a perfect recipe for a major repair or replacement.
Would you rather repair the broken bolt or do a major repair?
If the bike is your only transport then beg, borrow or steal something temporarily till you get the bike fixed...............................just kidding about the steal part.
