Not really. There are airlines who hire young low paid unskilled pilots, there are pilots from various countries with different English skills, there are pilots who didn't get enough sleep last night. Then there are airports that have different standards for security, different border-control waiting time, different luggage waiting time & equipment, different ground-crew serving the airplane. All this information is obscured from the passengers, but it doesn't mean it's not affecting safety, because it is.
Allowing individuals to adjust the safety levers means more people will die, because the vast majority of individuals who use air travel are not qualified or informed enough to make good decisions about these things. More people will die unnecessarily than under the current system.
People don't need to make those decisions. Currently, safety decisions are made by the government, which really doesn't have any competition and thus is not incentivized to improve its set of regulations. If you had 2-3 companies providing market review for the passengers, I'm pretty sure the situation would improve, not deteriorate. Perhaps some regulations simply don't make any sense and do not improve safety, but you'd never know that until you have one agency managing it.
Airline safety is currently in a state where it is nearly indistinguishable from perfect. Accident rates are so low that it's no longer possible to put an accurate number on the risk of taking a flight. And all of this has been done while keeping ticket prices at extremely low levels. It would be remarkable for any change to this to result in an improvement, since there's almost nowhere to go but down.
