Any attempt even remotely close to extreme enough to have any hope of being effective would require such invasive monitoring of computations run that it'd kill their entirely cloud industry.
Basically, you'll only succeed in preventing it if you make it so much more expensive that it's cheaper to do the computations elsewhere, but for a country at threat of military intervention of it's discovered what they're doing, the cost threshold of moving elsewhere might be much higher than it would for "regular" customers.
At which point you've destroyed your economy and created a regime so oppressive it makes China seem libertarian.
Now you need to repeat that for every country in the world, including ones which are intensely hostile to you, while everyone will be witnessing your economic collapse.
It may be theoretically possible to put in place a sufficiently oppressive regime, but it is not remotely plausible.
Even if a country somehow did this to themselves, the rest of the world would rightly see such a regime as an existential threat if they tried enforcing it on the rest of the world.
Somehow, no one is worried about the economy. Perhaps because it's the economy that's pushing this dystopian hellhole on us.
Even almost all the most locked down devices available on the market today can still either be coaxed to do general purpose calculation one way or another or mined for GPU's or CPU's.
No one is worried about the economy because none of the restrictions being pushed are even close to the level that'd be needed to stop even individuals from continuing general purpose computation, much less a nation state actor.
This is without considering the really expensive ways: Almost every application you use can either directly or in combinations become a general purpose computational device. You'd need to ensure e.g. that there'd be no way to do sufficiently fast batch processing of anything that can be coaxed into suitable calculations. Any automation of spreadsheets or databases, for example. Even just general purpose querying of data. A lot of image processing. Bulk mail filtering where there's any way of conditionally triggering and controlling responses (you'd need multiple addresses, but even a filtering system like e.g. Sieve that in isolation is not Turing complete becomes trivially Turing complete once you allow multiple filters to pass messages between multiple accounts).
Even regexp driven search and replace, which is not in itself Turing complete becomes Turing complete with the simple addition of a mechanism for repeatedly executing the same search and replace on its own output. Say a text editor with a "repeat last command" macro key.
And your reviewers would only need to slip up once and let something like that slip past once with some way of making it fast enough to be cheap enough (say, couple the innocuous search-and-replace and the "repeat last command" with a an option to run macros in a batch mode) before an adversary has a signed exploitable program to use to run computations.
Yes, this would be a substantial regulatory burden.