On the contrary. The sidechains would
My concern with sidechains isn't about their mathematically sound implementation, but rather with their effect on the incentives structure that has proven to work so well for the original Bitcoin.
If sidechains gain enough traction, they will form new clusters of gravity, which will begin tearing the idea of a single ledger apart fairly quickly with no one being interested in securing the main chain, which in turn would only accelerate the drainage of its value.
If that manifests, the niche that Bitcoin was created to fill will simply be left up for grabs and the competition will surely take the chance.
I was about to argue against this, but now I think I see how this could happen. To simplify, CoinX is a sidechain that gains a lot of momentum, so much so, that 90% of bitcoins become "locked" into it. At that point, CoinX has basically replaced Bitcoin.
While some might view this as evolutionary, what if CoinX sacrificied certain principles, like being semi-anonymous and fungible. Why would the masses flock to it if it made so many sacrifices? The same reason most people pay with a credit/debit card today.
That said, if someone can come up with the holy grail of anonymizing transactions, they could create a very beneficial side-chain. I've tried to think this through, yet found it very challenging because of the difficulty of achieving trustless at the network level.
Here would be an interesting use-case for a side-chain, though. The first eCommerce driver on the Internet was online gambling (next to maybe p0rn, which is basically free today). Not surprisingly, there is plenty of bitcoin based online gambling today. But, can you trust the casino not to cheat?
What if a gambling side-chain published all its bets on a side chain? You could not only verify that your bets were published, but do statistical analysis of ALL bets to verify the honesty of the casino.
Contrast that to moving your bitcoins to a casino, where you trust them with your bitcoins AND trust them to be honest, without any transparency or protection of your bitcoins.
To be sure, you could accomplish the bets chain today without changing bitcoin's protocol. The difference might be also protecting your bitcoins in the process.