[related] Has anyone considered the possibility of a Spectre-style attack in Ethereum's Turing-complete EVM? Not that the state would be unique for all contracts, but there's a possibility of communicating to an external contract with the output.
1) Worst case scenario, it only allow you to read the memory of systems running validator nodes. There aren't very many of these (tens of thousands perhaps) and they generally don't store particularly valuable secrets. A small number of them may store private keys to Eth accounts with a small amount of Eth, but that's not typical operating procedure.
2) The EVM doesn't have any internal mechanism for measuring time (beyond existing blocks), so any timing attack within the EVM would require some very clever way of measuring time.
However, the block-lattice cryptos like RaiBlocks that find a way to build in concurrency and shared memory might be different.