That is actually an interesting idea. The downside would be that it would effectively be a blocksize decrease as older nodes won't see POS blocks, only to see the relevant txns 20min later in the next POW block.
The POW blocks would still have to be one every 10 mins. Otherwise, the POW difficulty setting algorithm wouldn't work properly.
You would need a system that hits POS blocks every 10 mins too.
An easier alternative would be that blocks must be "stamped" with a POS proof within 3 blocks of being produced.
Stamped POW <- Stamped POW <- Stamped POW <- POW (working on stamp) <- POW <- POW
Each block would end up with both a POW certification and a POS certification. This means almost no change. You just need to come up with a way to do the POS stamps.
POS miners would build on the longest POW chain, but ignore blocks unless at least their great-grandparent (and earlier) blocks are stamped.
One characteristic of this system is that hashing power is useless between the time a POW block is found and the next POS block is found.
Yes, this has been brought up, although id like to hear from a miner why this might be an issue if all miners are affected equally by this.
It might not be a big deal if they can direct their resources elsewhere.
It potentially reduces the POW security by 50%. You can produce a competing (POW) chain with only 50% of the hashing power (ignoring the POS part).