The only problem is, Apollo, that many people are complaining about the system we have now. Imagine what it would be like to have ever more intrusive and time consuming inspections than the ones we have at present. Recently there was an idea, which thankfully seems to have been rejected, of feeling metal zips to ensure there was no weapon hidden behind! The airline industry does not need more reasons to discourage pax to fly.
Your idea would also inflate the already burgeoning TSA payroll. The TSA could actually buy the three major US airlines with its start up budget. This budget has not brought us security, 40% of test firearms continue to get through security screening. If a firearm can get through security the terrorists win. I know the securing arrangement on our cockpit doors would not stand up to a few rounds of FMJ 9mm. In this situation only a round going the other way will make any difference. By the way, a high power rifle in an aircraft is a REALLY stupid idea.
Yes we need better trained screeners and equipment but while weapons can still be smuggled through security and while they can still be pre-positioned on aircraft by minimally screened ground staff the armed pilot is the best back-up system. 68% of the US public agree.