Blockchains have a few serious disadvantages over other protocols (chaumian blinding, or just signed receipts, or a central ledger) -- inefficiency, lack of privacy (zerocoin addresses this, but at the cost of incredibly advanced mathematics), and the 51% attack.
Essentially, anything which is inherently centralized has no business being on a blockchain. This is really anything backed by a physical asset -- the ideas to do colored coins which were gold warehouse receipts were insane/inane. Most of the sidechain proposals I've seen are equally absurd -- the idea of equities issued in a blockchain where the equities are essentially tied to a single real-world issuer is an unnecessary step. You could just have the entity issue digital shares using a centralized protocol; non-repudiation works just as well with signatures. (you might use a distributed system for a virtual corporation of some kind, but that's an exception).
Bitcoin itself makes sense (it's a decentralized store of value), and some of the smart contracts stuff might make sense (but the smart contracts cease being self-enforcing, and thus smart, as soon as a lawyer or government gets involved...), but most of the sidechain proposals involve trying to recreate assets from off the blockchain in a less efficient, less secure way, just to prop up the value of bitcoin itself.
There's no reason to use a smart contract to "prevent issue of too many shares" -- you can just have the market price shares based on what the market believes is the outstanding treasury and float. People can build systems to provide better controls there, which might in some cases involve the blockchain, but it's not essential -- we can price assets using a market with imperfect information already.
A system with ~infinity of distinct issues, traded in realtime on market(s), with perhaps something like bitcoin as a unit of account, makes a lot more sense to me than trying to have one global currency (bitcoin) and then doing things like sidechains (which don't let you escape the limitations of the blockchain protocol).