[FifteenToes:]
"Oh God no, please.
If there's one thing Brexit has taught us, it's that democracy is only as good as access to information, and the necessary knowledge and ability to appraise that information. In your example, for example, there are all kinds of misinformation about the death penalty (how effective it is as a deterrent, for example) that people could make a bad judgment with."
Firstly, I suspect that if people could vote directly on certain general economic matters, we could see things swing more towards the left-wing side.
But anyway, with the death penalty example, yes, people could be misinformed on something like the deterrence effect; but that's likely also going to be the case if you have 600 politicians voting on the matter.
The average politician doesn't have the time/interest to personally research (what may be) conflicting studies, and weigh up all the different criticisms and arguments over the evidence.
They also, like the public, may well not even be primarily concerned with that. It's likely that many people would just vote on how they feel about it as a straight moral question: is it an appropriate and fair punishment to use for some crimes, regardless of whether society benefits from reduced crime. And politicians are no more experts on that kind of issue than the general public. No one can really be expert on that question in the sense that they have a special claim to likely having the correct answer. Or, in so far as you can have expertise in that area of philosophy / ethics / punishment, (i.e. having read plenty of material from different sides and being competent with assessing stuff), again, politicians probably don't even have that kind of limited expertise.
I'm thinking it's just going to come down to gut instinct on the moral question of whether it's OK for the state to kill criminals, exactly the same as if the general public was deciding the matter.
If you're against referendums, let me ask you a question... how would we switch to a PR voting system? I guess people aren't allowed a direct say over that question? They could be misinformed on the advantages/disadvantages of the different systems. So you don't want the public deciding this stuff. It's best left to the real experts in parliament.
However, if it's just left up to politicians to decide, they may be happy enough with the system we now use for selfish reasons. Why risk giving more power to smaller parties and letting them grow even bigger in the future as a result? Would the main parties want to vote for that when it could harm their own status?
Personally, I think we should trust the people (even though imperfect in their knowledge) with the question of whether they want a PR voting system or not.