Are sidechains intended to help Bitcoin scale? Do they reduce load on Bitcoin's main chain?
If not, why not?
No. They can increase scale, but that is not what they are good at or intended for.
Before giving a longer answer, let me first talk briefly about the difference between scale and scalability.
Increasing scale means increasing the throughput or number of participants to the system. It's very easy to achieve (decreasing the time between blocks, or increasing the size of blocks), but it would come at a cost of higher centralization pressure for mining and increased validation cost to the system. Whether these increased costs are acceptable is controversial, but there are certainly costs involved.
Increasing scalability means changing the system in a way such that increased scale comes with less increased costs. Known mechanisms for better scalability include better peer to peer relay protocols, faster digital signature systems, software improvements, technology on top such as payment channels or lightning to reduce on-chain transaction need, ...
Sidechains don't improve scalability. If we want the same security level with sidechains, the same amount of people and miners need to be validating them. That is at least as costly as just increasing the block size of Bitcoin itself, and sidechains come with extra compromises on top of that.
So, sidechains may increase scale, but are not better at it than larger blocks would be.
What sidechains do bring is the ability to experiment. To be able to build networks that run on different - and possibly better-scaling - technology, but without needing to first beat bitcoin's (the currency's) network effect.
Sidechains are intended to improve scalability, but only indirectly: by enabling innovation. Not because they can just offload things from Bitcoin.
Sidechains don't increase scale without changing the security. However they could allow people making lower security (e.g. lower value) transactions to opt-in to use a higher scale, lower security chain. The security would be lower for two reasons: because the security model on a side-chain is slightly different than main chain, and because if the sidechain has bigger blocks, we would expect less people to validate it, so it would be more likely to suffer policy attacks.
Given that about 45% of Bitcoin's 30-40% full blocks are values under $1 that could perhaps be of interest to many types of application and allow practical scale and be a reasonable tradeoff for many people.
For example I might say: put $100 in a sidechain with bigger blocks, and top it up when it runs out, with the intent to use that as spending money for small value items: tips, cup of coffee, VPS service, etc. I would be happy doing that because basically I could afford to lose $100. Also spending money is not at significant risk of political attack, and there is less risk of political attack because there is a recourse: if your spending money wallet coins were politically attacked, you could move them to the main chain. The attackers would know this and therefore also be less likely to try the attack.
So while it's not a silver bullet and doesn't reduce the amount of bandwidth, it is a potential option people may start to try deploying as federated or full p2p sidechains technically come online. (There is a testnet federated sidechain that has been online since Jun 2015.)
One argument can be that if there are a lot of fees on the sidechain then someone who has bandwidth only to verify the main chain, would receive less profit, and maybe become unprofitable and so have to stop vs a bigger miner with more bandwidth. However it is possible to pool mine the sidechain and self-validate the mainchain, and so collect the sidechain fee reward via a pool and be equally profitable though not helping with the level of decentralisation security of the sidechain.
This kind of higher scale sidechain is strictly optin for security, it is the recipient that choses which chain their receiving address is on. It is also backwards compatible (though the details are a bit more complex) so someone on the mainchain who receives bitcoin from someone on the sidechain, they are at no elevated risk of losing those funds if they chose to stay on the mainchain for decentralisation security reasons.