People can see who pushed for certain parts of an agreement then not vote for them again extinguishing their political power. That’s why we have journalists investigating the inner-workings of parliament.

That’s not at all how politics or investigative journalism work? Those would be closed door negotiations. If you read news from PR systems (DW, any reporting from Israel) you’ll learn that while parties broadcast their broad positions, the specific horse trading is quite secretive.

actually end up rewarding the questionable party with more seats even if the public reduced their ballot support

As also happens in PR. Say last election happened under a PR system with the Conservatives and Bloc being thr party with thr most seats and a partner to push them into majority territory. You’d then have what I presume you’d categorize as an extremist party combined with a purely regional party making decisions for everyone.

This is why Netanyahu, despite being wildly unpopular, still has a pretty good chance of winning elections; small dogmatic parties can combine with several moderately popular ones to control a country. It’s a horrifying situation with zero accountability, whereas we know exactly whom to blame and punish accordingly.