Kizhaz post basically sums it up pretty good.
By changing the rate to 1/8192, you don't just increase the amount of rare shinies thus making them affordable. You also increase the amount of uncommon and common shinies to such an extend that they'd basically become worthless. With so many people playing at the same time, a lot more shinies would be found resulting in the complete collapse of the shiny economy with very few exceptions.
Sure there are upsides to it too. Cheaper shinies, creatng competitive shinies (though they wouldn't be unique because everyone would have access to them), having more rare shinies around (which can also be a bad thing as the rares would eventually become semi-rare or even uncommon [ex: Snorlax]), and of course, finding more shinies in the wild. But then again the excitement also would shrink quite a bit each time as they'd pop up even more than they do in some cases today (looking at you, jajas).
Having cheaper shinies isn't always a good thing either. Look at Lucky Eggs for example. They were rare and desired, until there was much more supply than demand and their value plummeted. Sure they're still useful, but nowhere near as desired as they once were. The same thing would happen to shinies.
Want to sell your brand new shiny Vuplix because you need Yen for comps? Too bad, there are already 25 other Vulpix' on the market. Now what happens is you'll all undercut each other, making the value decrease more and more until the point where good comps could be worth more than the brand new shiny you just caught. Tl;dr basic economy.
Everything would evolve around rare shinies, and those with rare shinies wouldn't even think about accepting the commons everyone and their nans have 8 of now. So now what do you do? Go hunt rare shinies yourself. And 200 other people do the same. And now that rare shiny is becoming semi-rare. It's already happening to a certain extend with the Charmander line. Of course it doesn't affect the value too much because of how desired it is, but if you seriously have a look at the pure number of shiny Charmander and evolutions that are around, it makes you wonder what would happen to all the other good shinies out there.
Doesn't sound that good anymore, does it?
Negged for a bad idea.