there are no guarantees in life. through my little bit of research i have come to the following conclusions:
1) once you remove the governor all bets are off
2) there is no time or rpm limit on when or if a failure will occur
3) some "stock" go kart classes run their karts with "stage 1 mods" with no issues, chainging the rod out every 2-3 races.
4) if you do not check clearances, and hone the rod, you may cause the rod to seize and break due to oil starvation from the lack of lubrication at high rpm.
5) if you rev too high, the magnet (which is held on by a screw and some glue) can fly off and cause the magneto to break off and/or flywheel failure
6) anybody who says it is "safe" to run without a billet flywheel and rod after governor removal because of "insert anecdotal personal experience here" is a person that is ok with exposing themselves to a liability. The liability is your health and safety. Not many people are going to come out and say its safe or not safe at a given rpm because there is no clear consensus on what is or is not safe because sometimes thigns break and sometimes they dont. Asking for a finite answer is not going to get you anywhere. Nobody wants to say you should go ahead and send it, only for you to actually send it and the next thing you know you have a piece of aluminum or steel shrapnel hitting you in the shoulder, or leg, or worse. Is the risk of permanent serious injury really worth the cost of a safe flywheel or safe connecting rod? Im sounding old, but the more and more I see and learn about this, the more inclined i am to put a billet rod on there at a minimum, and a billet flywheel on there with any serious modifications. It only takes once to screw your whole life up and hindsight is always 20/20, shoulda woulda coulda.... they come pouring in after the fact.
Onto the gray area
If you didnt remove the governor, but backed out the throttle stop, you could actually rev to 4300ish rpm on a non hemi and 5200 ish rpm on the hemi. I have found this out experimentally.
Now I personally have ran engines without billet but only under load. If you "free rev" the engine, it floats the valves much faster. When you are floating the valves hard, the valves actually can bounce off of the seat and this causes, at best, premature wear on the valvetrain and can mushroom/distort the valve and seat, which causes loss in compression and power.
If you put in heavier valve springs, oil clearance becomes even more important. Any reputable engine builder will check oil clearance on the crank journal and hone the rod. The hone and measuring tools used to do this cost more than a $60 billet rod and some plastigauge....
If you advance the timing, by putting in one of those advance keys, you will have to torque the flywheel back to spec. If you undertorque it, the flywheel will spin on the crank, if you overtorque it (e.g. impact it on there), the flywheel may in fact shatter prematurely due to internal stresses and possible cracks. You must use a torque wrench and torque to spec.
If you put in a nice cam, you will get into the danger zone very quickly, and the more rotating inertia an engine has, the bigger the failure will become.
How much would a hospital bill cost? I can gurantee that it will cost more than the $160 it will take to prevent your engine from grenading at high rpm. What kind of loss are you prepared to take on because you wanted to save a buck? This isn't some fairy tale or myth. Once you are in the grey area, you really are gambling with your health and life at that point.