A properly set up and maintained Honda engine should start on the choke at full throttle within three or four pulls and should run off the choke almost immediately. Sounds like the rental shop isn't doing its job. Tell them you want your money back but that you'll be happy to rent it again if they tune it up first and get it running right.

yeah those honda's are finicky,because they're jetted too lean.....

They need to be jetted lean to meet emission standards. I agree with Fred, the yard is not taking time to ensure the fuel system is clean. They are likely turning it around quite quickly.

this is one reason I always get them to start and run the machine before taking it away.