Bumping this to see if someone can answer the question. Ty
To answer your question you just need to read up on the DAO debacle.
Waves Platform is also launching Smart Contracts and sits on the fastest decentralised blockchain in existence. These also will be non-turing although Turing complete SC is on the roadmap this year.
Only very few applications specifically need Turing Complete - in most real world cases the logic required could be off-chain. The jury is out as to wether the inherent risks outweigh the benefits of Turing-complete on chain - however DAO was a prescient precedent.
https://en.wikipedia.org/wiki/Turing_completeness