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Afaics, this is not secure for reasons:
1. The block reward is much smaller than the rewards on the main chain, thus unless the side-chain uses a different mining algorithm, then the main chains miners can 51% (or 33% selfish-mining) attack the side-chain. To incentivize sufficient security, then side-chains will not be competitive with coins kept on the main chain (or a different consensus algorithm which doesn't need to spend so much on security as PoW does, which is my yet unpublished design because of lower sunk costs as compared to PoW).
2. An attacker can yoyo the difficulty of the side-chain by moving many coins into and out of the side-chain. Difficulty attacks either leave a coin with periods of being very slow to confirm or enable the attacker to 51% attack during periods of very low difficulty.
There are likely other problems. Side-chains are simply a broken concept.
1) The point is that we now have a smaller chain that can be secured independently of the main chain using POW. It can have the same POW or a different POW or as stated above even a different consensus solution. Demurrage in this context simple provides source of coins eliminating the dependence on fees that lies at the heart of the long term security problems not only of side chains but also of most POW coins. As for the side chain being competitive it may trade security on the main chain for other advantages that cannot be implemented on the main chain, are judged to be too risky to implement on the main chain, or even competitive markets between side chains. One does not need the same level of security for all of one's money. There are tradeoffs here and the market can judge what works and what does not work.
2) These type of attacks can be addressed by having a non refundable cost associated with moving coins into the side chain or out of the side chain.
I would be careful with statements such as "Side-chains are simply a broken concept." In any event, I have introduced demurrage into this argument and if anyone gets the idea to patent this here is the prior art.