So... add more car services? What!? Grade-separated rapid transit (ideally with platform screen doors), aggressive congestion charging, parking maximums, and general Copenhagenization - these are actual solutions, not more cars.
I mean, the rest of your comment stands - I don't know of anybody who got hurt on my street, but that's probably because my street is only open for cars between 8 and 11 (AM, for those of you stuck with 12h clock).
But platform screen doors, nope.
I feel like they would be reduce incidents of people/things falling into the tracks as well as help with queues in front of the doors (i.e., people know where to queue, as opposed to just following the train until it stops).
In practice the incidents are rare (even in case of metros, it's something you read in news papers every time it happens), and the few attempts to implement them were generally underwhelming. And, if anything, the risk of a person getting between them and the vehicle means you're just swapping risks around.
So yeah, they're costly, of dubious use, they're yet another part that can break, and a general eyesore. And, if you want dense networks (and you do, trust me on that), then increasing the amount of space required for a stop is also a Bad Thing.