I wouldn't say aerodynamics kill overtaking per se, but certainly aerodynamics generated from wings struggle when they are in a turbulent wake from a car ahead in a corner.
They absolutely definitely do kill overtaking. If we look at something from the opposite end of the spectrum, like NASCAR, where downforce is almost nonexistent, you following behind me benefits you in that it reduces air resistance on your car, making you faster, but without any negative consequences since your car doesn't really rely on downforce for track performance. Now, if we swap our cars and instead run F1 cars, 60% of your performance comes from the chassis and its aerodynamics, so while drafting me may reduce drag, you lose a lot more performance because the dirty air cripples your wings' effectiveness. So, while in NASCAR you're benefited by drafting behind me, in F1 you're penalized by doing so.
I used to be against the concept of DRS, until it became clear that, in a lot of cases, it is a tool for the driver of the slightly faster car to use to pass the car that might've otherwise held him up.
DRS doesn't just hand out free overtakes to drivers anyway. Usually drivers close enough to use DRS and doing so still run lap after lap without actually overtaking anyone. Last year, I believe in Spain although I can't say for certain, Button was trapped behind somebody lap after lap after lap, on every lap employing DRS along a long straight but always running out of road just shy of being able to complete the overtaking maneuver. Without DRS, he'd never even have been able to fantasize about overtaking there, and even with DRS was unable to pull it off for many laps. DRS only makes overtaking somewhat more possible, as opposed to handing out free passes.
That's part of racing. Why not just show blue flags if the car behind pulls a faster lap?
That would then be awarding free overtakes. Drivers are supposed to work for those, and even with DRS they still have to work for them, as I've pointed out.