As someone else alluded, I think this "Yes you can run it without a blade" / "No you can't" confusion is caused by the presence or absence of a cast iron flywheel. Back in the day, I think most B&S engines, regardless of application were built with cast iron flywheels which provided the necessary rotational inertia to make the motor run and run smoothly even with nothing at all connected to the output shaft. Don't know about older other brands but I suspect that might have been the case for them as well. Eventually, someone figured out than in certain applications (lawnmowers with fixed attached blades for one) that the fixed external rotating mass provided enough of a flywheel that a cast iron flywheel wasn't needed (and if you don't need it, making the flywheel out of Aluminum can save a substantial amount of engine weight and lower the engine cost without compromising performance). So, newer lawnmower engines are likely to have aluminum flywheels and will either not run at all or will run poorly (at least on mowers where the blades are attached right to the output shaft).
All vendors (Honda, B&S, Techumseh, etc.) still make engines with cast iron flywheels for applications where there is not sufficient fixed rotating external mass (ride on mowers, horizontal shaft generic engines, tillers, etc.). Naturally these engines will run with the output shaft completely disconnected from everything.
From the OP's fix, it seems clear that he simply bent the blades which therefore became in essence a very badly balanced flywheel. The suggestions to check the half moon keys were good ones though, I've had partially broken or sheared half moon keys stop a motor dead in it's tracks after hitting something, sometimes even when I thought that it didn't take that hard of a hit.
