That's actually precisely what the Patent Office does now.
https://gigaom.com/2013/03/18/first-to-file-patent-law-start...
It's even worst for the world of software, because pretty much any piece of software will eventually be independently developed by someone else, yet the one to first file for it will get to reap all the rewards.
Well, in practice others get to do it, too, while hoping they don't get sued, but that's just because of selective enforcement - if the patent law was enforced 100% of the time the system would quickly break-down.
For instance, I think there once was an article on Bloomberg about a smartphone containing 250,000 patented inventions. Even if say 80% of those were expired (I don't remember if it mentioned that older patents were included), nobody would be able to make a smartphone, unless each unit cost like $10,000, so they could afford to pay everyone.
But the patent system isn't anywhere near being enforced 100% of the time, so we limp along with it broken as it is, with only a few companies getting to rip-off those making the products, because they "own the patent" (while most of them don't even have their own similar products).
Think of it as a well-formedness check rather than a content validator. Patents don't have to be able to hold up in court under scrutiny in order to be issued.