Motorcycle engines have the transmission built into them so you would have to run it thru the tranny too. Couldn't use a regular pump or love-joy setup. I'm sure it could be done, but from a cheap standpoint why not just get a junk lawnmower engine. A lawnmower engine has all the mounts to make it work with off the shelf parts so no big headaches trying to fab up the pump mounts. And a lawnmower with a blown transmission, rusted out deck and 4 flat tires would be way cheaper than a totaled bike.
Again, not saying it can't be done, and if you want to make it work so yours can be different more power to you. Just saying a cheap wrecked bike can seem like a good deal until you add up the cost of making everything else fit your cheap powerplant.
One other issue that would take time to correct is the governor issue. The engines used on yard equipment and splitters have a built in speed control/governor. When you attach the cable you are pulling on a spring that speeds up the engine - and the built in governor controls the throttle setting to hold that speed. The governer adds throttle when the load increases and then takes it away when the load is removed.
The governor issue can be addressed and there are add-on governors that can be adapted. I had toyed with the idea of using a small car engine or bike engine for a generator - but I finally decided that it would be too involved for the rare occasion that I lose power for any length of time. The store-bought generators work just fine for that occasional use - even though a BMW or Harley motor would sound so much better!
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