There are many systems, the Australian Federation of independent States adopted a "Washminster" system based on both the UK Westminster system and the USofA Washington system.
Popular election of senators in the senate / upper house hasn't been a disaster there.
The Australian Electoral Commision as an independent body does a lot of heavy lifting towards keeping the washminster system running (no gerrymandering and a world class voting system).
Independent checks and balances are an essential part of any system of government.
The people vote in Representatives to debate policy, an independent merit based civil service carries it out, overwatched by independent scrutineers, judged by and independent legal system and enforce by a spectrum of LEOs and peace officers.
A feature of the Australian system (IMHO) is how rapid the churn on Prime Ministers can be ... the Washington system by contrast can't even toss out a corrupt felon grifting hard in public view.
The AEC did nothing to stop the Australian government trying to criminalize the views of its political opponents, so it's not doing all that much heavy lifting.
Popular election of senators in the senate / upper house hasn't been a disaster there.
* https://en.wikipedia.org/wiki/Australian_Senate
Australia also has political weightings wrt various regions populations.