However I don't understand your proposal for thin miner there. Double spending is already checked via index lookup, however you need the index in the first place, then in order to trust the index you need the block chain as proof.
Could you describe your proposal for thin miner a bit more?
Sure... I'm kinda too bored to describe it completely, though, so a quick summary:
As you've noted, currently node builds UTXO database and looks it up when it checks transaction validity.
Potentially we could use "cloud database" (DHT, for example) instead of a local UTXO set, but there is a problem: we cannot trust this "cloud database".
So we are going to put some extra information into blocks, and that information will help us to verify data we get from "cloud database".
This information is simply a list of outpoints spend in current block arranged in a tree fashion so it can be easily searched.
When client receives new transaction it checks its validity: each outpoint mentioned in transaction inputs is looked up in DHT to check whether it even exists. If it does exist, we need to check that it isn't spend already. To do that, we identify a bin associated with this outpoint, find current top of that bin by doing search in last N blocks (which requires some information in block body, but not full blocks), then we fetch enough history for that bin from DHT to confirm non-existence of double-spend.
It is true that this process might be significantly more computationally expensive than lookup in a local UTXO database. However, storage requirements are drastically lower.
So effectively it is a trade-off: higher per-transaction computation and communication costs vs. high storage and initial blockchain processing costs.
However, it's not so simple: this approach potentially allows distributed processing where miner will include transactions it can verify inexpensively. E.g. suppose miners will pick a set of bins they specialize on, and we'll have small blocks touching only handful of bins instead of huge-ass blocks touching all bins.