RE: What are the side chain settlement solutions?
private vs. public

Blockstream = Lightning Network 'private' side chains for the BTC big boys.

LoLz
It works until one of the partners screws up on settlement.

But already there are operating ALTs that can function as 'Lightning' forms of settlement and clearing houses just unwind/trade back to bitcoin positions as they please (in 45min-12hr windows) .... you know at bitcoin confirmation speed.

XRP is designed to do this. But seems to have forgotten.
DASH could do it.
STELLAR is better designed to do this.
BTS, NXT, XCP, PeerGroup, and XEM can create 'pegged' assets to do this.
NuShare and Omni already have 'pegs' that appear to work.

A wide array of ALTs can collectively serve to do this ... all in the open public market arena.

Well seems there's been lots of smoke blown in to the digital universe.  
Private Side Chains are raising $millions in VC monies, is the why.

Public side chains are already clear and present.  So correct ... "Why don't they?"

CW still wants to 'discover' and get in on the 'next bitcoin'.
Rather than look for sidechain (cough ALTs with fast block speeds) as a means to transmit BTC like lightning quick.

That means (basically) one giant global order book, where a 'cartel' of popular btc exchanges via 'side'chains (cuz can't omit that ALTs could do it) weave all the markets into one real time eXchange ... and can settle up (at least mostly) in under 60 seconds with ALTs and unwind that 'agreement/contract' as soon as bitcoin can be sent.