It's not a foolproof system, but I think most of the cases you'd find about 'dodgy evidence' would also mention a 'overly close relationship between police and prosecutors' - because fully independent prosecutors should be rejecting cases with dodgy evidence. The police can get a bit grumpy with CPS for being quite strict at times - but it holds them to work their next case properly.
The PO clearly managed to convince the CPS in a number of cases, but had they had to do that for all there would have been a lot less cases prosecuted in total, and I think there would have been questions about their system a lot sooner.
It might not have avoided the problem, but it would have been much needed additional oversight into what they were doing.
So the separation of powers isn’t a magic solution to the problem then.
The lie came from the fact they weren’t looking into their own evidence and realising something was up when they were prosecuting hundreds of sub-postmasters.
There were a (relatively) small number of prosecutions from the CPS as well, which suffered from the same problem: the Post Office investigators gave the same bad evidence, which they used to convince a jury to convict.
I don't see how separation of powers helps here. I'm sure if I looked, I'd find cases in the USA where the police and/or prosecutors told a pack of lies based on dodgy evidence to secure convictions of serious crimes, too.