Done the way I suggest, you would be able to get on pretty much any ride you want. Right now the reason FPs disappear so quickly is a lot of people book then just in case and then never even show up to the parks.
Seriously, at
Disneyland, there are only a couple of FPs that disappear by around 2 PM or so. Many attractions have return times that are available for almost immediately use. And there aren't as many attractions with FP as at WDW. Day of only would also reduce stand by times to more manageable levels, as Disney would have to staff the attractions better and run at full capacity because they wouldn't know in advance what rides were going to be busier at what times.
This also would potentially mean more people in queueus and less clogging walkways, etc. At any given time, making the parks feel less crowded.
Having used both systems a lot, the day of system actually greatly reduces wait times and how crowded the parks feel.
At Disneyland, even if I don't show up until Noon, I can still do around 10 attractions by about 5 or 6, including some of the more popular ones like Guardians or Racers.
Abd with Disneyland you can only book one FP at a time, once you use it you can book another. Alternatively you can also book another after a certain time, this usually only comes into play if your return time is more than an hour and a half away, so technically under certain circumstances you can have multiple FPs, but that is rare.
By having these limits in place, it prevents FPs from running out at Park opening and at WDW the chances of them running out for any given attractions would be far less due to how many attractions have FP and the higher capacity that Disney would have to run at, along with the reduced Standby lines at many attractions.