I think this overstates the case. Up to 40% of murders go unsolved in any given year. Most murders are committed by people the victims know, that's why they're "easy" to solve. If you don't know your victims, there's virtually no way for the police to link you to the crime unless you make a colossal mistake, like divulging our identity or your contact info to the person who hired you, as the police will be looking at them closely.
DNA and fingerprints, unless you're already a criminal where those are registered, would only establish you as serial murderer whose identity is unknown.
Or a cop happens to be sitting one street over and hears a gunshot and gets to the scene just as you're stepping out of the building.
Or the victim is paranoid and has an itchy trigger finger.
Or the cops are investigating the victim's family and associates and notice a weird pattern in their bank account.
There's a lot of ways a killing can go wrong. Even if the odds of any one killing going bad are small, the cumulative chance of an error creeps up with each job. Worse, it's hard to jack up your prices really high to reduce the number of jobs you have to do because the more money moves around the more scrutiny it receives.
Interesting that you assume an assassin's preferred method of execution is a gun or other violent means of execution. That seems like the last resort of anyone competent to me.
A bigger problem might be that it's not as easy to for sure kill someone as most people think, especially if you want to avoid leaving any evidence at all. It only takes one error to kill your career. It also doesn't help that the public's image of assassins (super professional bald guys with enormous resources) is pretty much completely wrong. Actual assassins are much more likely to be drug addicted flat broke bums.