That question might sound completely trollish but it is not. Imagine that eventually all nodes are turned off except for a single, centralized supercomputer which did all the contract-executing work. (Mining would still be decentralized.) What would be lost, security-wise, under that scenario?

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This question is hard to parse because you say mining is still decentralized, but a centralized computer does all the contract-executing work. In the current design contract execution is the main function of mining, so it's not clear what you're thinking the miners would do.

I suppose you could have a network where the miners just did time-stamping of transactions rather than executing scripts. In theory you should then be able to make script execution completely deterministic, so anybody could set up their own node and run the transactions in the time-stamped order, and in theory everyone should be able to get the same result. But you wouldn't need that to be a single central node; Anybody could run a node that ran the calculations.

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