Practically speaking to transfer an existing chain to a sidechain would be nearly impossible. You would have to transfer all the value of the altcoin to Bitcoin and then to the sidechain. This means that somehow people would sell their altcoin for bitcoin to transfer it onto a sidechain. But how would that work? If an alt-coin was "moving" to a sidechain no one would be willing to buy it. The particular alt-coin community could devise some kind of a scheme to transfer the value, but there would always be unforeseen consequences. (look at the Ethereum DAO-hard-fork fiasco for an example)
Think about it like this: what if a country A decided to get rid of its currency, lets call it A-dollar and instead start using USD. In this case you would tender your A-dollars to the central bank and they would issue and equivalent amount of USD to you. This is only possible (in theory btw) because there is a central authority. How would this work with a decentralized currency?
These are just some high level thoughts, as usual the 'devil' is in the details.
Let's say Ethereum becomes a Bitcoin sidechain. Let's say people want to "move" $100M worth of Ether from the Ethereum sidechain to the Bitcoin mainchain. How exactly would that work? Remember, there was no Bitcoins "locked in" to Ethereum initially. If you change the mining reward now, there is still $1B Eth on the chain without any corresponding Bitcoin... – Atte Juvonen – 2016-09-15T21:40:12.947
1I don't believe anyone would retrofit their alt coin to become a sidehain. That would be extremely contentious for holders of that coin. Instead, a sidechain with the same purpose would be created using Bitcoin as the main chain. If it takes off, then the original alt would lose value, as its purpose is fulfilled in a cheaper and more interoperable manner as a sidechain. – Jestin – 2016-09-15T21:46:04.297