As one BYC'er so accurately described it, once the shredded paper gets wet from their waterer and their poo, it makes paper mache'. Fun if you are in to some really strange crafts, but not alot of fun to clean up.
I wouldn't use shreaded paper. I tried it too, and it didn't work out to well for me either, so i got some pine shavings and sprinkle DE in the shavings and no more mess.
We have some in our layer boxes...and we find that it tends to stick to the eggs. They end up looking like they have been to a wedding and got caught up in the confetti cloud.
Next to shavings I consider shredded paper to be one of the worlds worst substrates for bedding chicks.
If you never want to lose a chick from having the bedding eaten, Wood Pellets are the best thing to use. I use newspaper or paper towels just one day placed over them with feed scattered on them to get the chicks started eating. I remove it the 2nd day and put in a feeder. I have started a thousand + chicks this year and can count my total chick losses on the fingers of one hand.