As ZB has pointed out, the exchanges do happen on the same, single Bitcoin ledger. That ledger is merely fragmented into different chains. The value is distributed on different chains but is all, in theory, compounded into the same network/ledger.
The problem I'd like for you to address re: federated SC's is they have the same consequences of changing the economic incentives for miners. Yes that change does not happen on the protocol level but it is IMO at least equally concerning. In that scenario, the incentives are not adopting a different model but are effectively "hijacked" by the federation/oracles/OT. This has the potential to considerably decrease the miners incentive to protect the network, especially compounded with the block subsidy drop.
If we expect miners to depend on transactions fees in the future then should we not make sure these transactions are not driven away to schemes that are out of their reach?
But a decentralized SPV proofs managed or secured by the same scheme as Bitcoin, entrusts the securing of the money in a service or a business to the network. That sounds good but it introduces an additional risk, you now have to trust the entity to deliver on its business and you have to trust no conflict of interest arises in the network, you have acknowledged that miners would have new incentives and it would be possible to abuse those privileges, however unlikely that would be additional risk in the quality of the money.
I don't think Satoshi designed the existing incentive structure in expectation that transactions would emigrate "off-chain". Of course this is bound to happen but it is a dangerous proposition considering the overwhelming demand that can not currently be accomodated on the mainchain and would become out of reach of the miners.
The chains secured by decentralized SPV proofs should not be ones that are "provided" by a service/business. IMO the likely outcome is that these will be utility chains that are open-source and certainly not proprietary to any entity that I need to trust for anything.
Any business willing to offer a service on a sidechain would be wise to consider the federated model for obvious security reasons and the need for oversight that you have pointed out.
Moreover, the new incentive model does not necessarily translate in new incentive to abuse their privilege.