Than that means that the cost of the Checkpoints would be the minimum fee of the POW chain to sign the transaction of the latest checkpoint. What about size of the POW chain and connecting to it without storing the full chain? SPV node system? How would that effect memory usage?
Hmm.. not sure.. let's think.
As far as the checkpointing. Assuming you would want to store a checkpoint every 24hrs for you POS chain, and that there were 10,000 different POS chains running of it, that would be, well, tiny. Easily fits into 1mb blocks..
Other txns could be cross-chain transfers, going from one side chain to another. This would need to go through the main chain, but it would not be a daily occurrence for most users. I can't really say how much of this would happen without knowing what chains were running.
The main chain would really just be a clearing house. All the 'Action' would be happening on the various sidechains.
So it might be quite an expensive min fee on the main chain. But that's OK, as the fees on the side chains could be tiny. (I think this is the current position being pushed by blockstream..)
As far as running a node, I think it would be no different from now. Just that you could run the main chain node, or a side chain node, or both in some merged-mine hybrid.
Main Chain SPV clients would be fine, but as I said, I think most of the daily user action would be occurring on a side chain, so they would not be as prevalent as on Bitcoin.