There's decades of academic work in the form of "impossibility" results showing that handling byzantine fault tolerance in distributed consensus is alot more computationally expensive than omission/crash fault tolerance. The following (FLP impossibility result) being one of the most famous ones:

https://groups.csail.mit.edu/tds/papers/Lynch/jacm85.pdf

Yes, that's the root of the problem. A deceptively simple sounding result.

Related: Bitcoin is [x] distributed [x] secure but NOT [] fast. It is a global clock that self-adjusts to tick roughly every 10 minutes, and that tick is used to extend an immutable ledger by adding verified transactions to it. The tick-time is chosen to allow for global propagation to happen. Incidentally this global clock can be used for other things than sending money, such as cryptographically tying something in the real world to a point in time.

I don't think there's a formal proof, but the idea has certainly been entertained. The scalability trilemma might be what you're looking for:

https://multicoin.capital/2018/02/23/models-scaling-trustles...

can you propose a formalism for your notion of "fast"?

As fast as a system which is either distributed or secure?