Well, the wheels don't fall off just because the max payload is exceeded by 1 lb. Or even 100 lb. Exceeding the payload rating is like walking out on thin ice: the more you weigh, the riskier it is, and the further out you go the more likely any fault may be severe.
In many cases the payload limit of a 3/4 ton truck is a suspension and tire limit, in which case suspension assists and bigger tires can do the trick. Another shadow-factor is that 3/4 ton trucks are usually GVWR-rated to stay under the DOT guidelines for weight class. Many states draw a line at 8600 lb GVWR for an increase in regulations and/or driving license class, plus the federal DOT uses GVWR to determine when regs for marker lights and other "big truck" requirements kick in. Thus it is possible that the Payload on a 3/4 ton is artificially limited by its lower GVWR.
The difficulty in all this is that it requires a detailed understanding of the mechanicals of the specific truck. Most people aren't knowledgeable enough to do that, and the data as to why the limit is what it is is near impossible to obtain. Therefore exceeding the Payload rating is a gamble and anecdotal stories from others about the benefits or dangers of exceeding payload are pretty much useless when considering your own truck and trailer.
Your insurance worries are baseless. Read your policy - there is no clause that says no payout if the owner or driver is negligent or foolish. Your insurance still covers the vehicle if you are reckless or drunk or any other foolish action. An extended warranty contract, on the other hand, will likely deny reimbursement if there was contributory negligence that may have caused mechanical failure. You are also more susceptible to civil suits for liability if you have exceeded recommended limits, whether speed or weight or customary practice.