Since it is to some extent a numbers game, yes, academics (especially newer ones looking to build reputation) will submit quantity over quality. More tickets in the lottery means more chances to win.
I'm not sure though how you change this. With so many voices shouting for attention it's hard to distinguish "quality" from the noise. And what does it even mean to prioritize "quality"? Is science limited to 10 advancements per year? 100? 1000? Should useful work in niche fields be ignored simply because the fields are niche?
Is it helpful to have academics on staff for multiple years (decades?) before they reach the standard of publishing quality?
I think perhaps the root of the problem you are describing is less one of "quantity over quality" and more one of an ever-growing "industry" where participants are competing against more and more people.
In what sense? If you put it on a website, you can publish a lot more without breaking a sweat.
People who want a dead tree version can print it out on demand.
The scientists themselves are working as reviewers.
More scientists writing papers also means more scientists available for reviewing papers.
And as you say, distribution is easy, so you can do reviewing after publishing instead of doing it before.
Just like what we are doing with blog posts or web comics or novels.
Replicating research is already difficult. Finding quality research under the publish first approach will be like trying to find a needle in a haystack and I fear considerable research will be wasted on dead ends.
I don't think I ever heard anyone complain that eg Arxiv makes replicating research harder?