It takes minutes to self publish a book on Amazon. Because of this I'd imagine publishers are not as flooded as they used to be.
https://kdp.amazon.com/en_US/
It has been joked that every single person who lives in LA has written a screenplay. While not 100% the reality it is not far from the truth. It is a concentrated saturated market. If you were to dig through the trash of a studio you would probably find a whole ton of screenplays. If you take every little town in the US there is usually someone who drives to LA with the dream of becoming big in Hollywood. And really these people come from all around the world. That's a lot of people with a lot of dreams. That's why Hollywood Blvd. is called the Boulevard of Broken dreams.
Book publishers are still bombarded by scripts, but I wouldn't say as much as people in the LA area with screenplays. There are several publishers all around the world, which lessen the load for any publisher. People don't need to find some fancy publisher. The only thing however a real publisher can be good for is creating publicity. You don't really get that with amazon.
I couldn't give you numbers, but have read books on getting screenplays made. I've read accounts from agents and producers that had to wade through countless scripts and simply threw most of them in the trash. The sad part is I'm sure some great scripts get thrown in the trash that are merely unappreciated. I even read one account where a script was thrown away because it didn't use the proper type of metal brads or everything else was fine about the script but the font wasn't Courier. The nerve!
That isn't to say that there won't be a future one day where making movies won't get to be as easy as publishing books are now. This is an indy forum. So, if you intend to make your movie with indy production in mind it is highly likely to get made as there are few barriers for that. Writing the next installment in the Aliens Series or anything really expensive is a difficult goal though. Even Neil Blomkamp who was able to get his foot in the Hollywood door is having trouble with that.
A nice thing is right now it is not terribly hard to set up your own streaming channel on a Roku that competes with netflix and hulu, or even publish a movie on Amazon or Youtube.
http://www.indietalk.com/showthread.php?t=63645
In that thread I show you how to get a channel set up. It only took me a few hours to make my experimental channel. It isn't the greatest, but it is a start. I don't really have my own content though. When you launch your own channel you become a movie distributor, which is something people would not have been able to do a few years ago themselves without a lot of money. If you have films you have made that you have the rights to you can create a space where you can start making money off of them. If you do please give me the channel name I'd love to watch. You can make money off of commercials or paid subscribers. I'd start off free though. You give out crack for free and once people are hooked then they become loyal customers.
Also, things like Kickstarter have helped people launch some films. We're living in the time of the democratization of media. When you think about the studios at some point they were all little independent companies making silent films. One of us is going to be the next Carl Laemmle, William Fox, Warner Bros, or Walt Disney.