"Republic" and "democracy" are not antonyms. This was a bit of linguistic prescriptivism put in by the John Birch Society that I feel the need to correct. "Republic" just means that the head of state is elected and "democracy" just means that there's voting. Whether they're voting on individual bills or voting for representatives, it's still democracy. Hell, people in the UK refer to themselves as "republicans" because they want to get rid of the monarchy, not because they oppose direct democracy.

The problem with state-appointed Senators is that it was warping gubernatorial politics. If you didn't like your Senator, you had to have the state governor replace him, and in practice most people were treating their vote for state governor as a senatorial vote anyway. Direct election of Senators just cut out the middleman.

Furthermore, we should be very careful with veto powers in a democratic system. Have you ever heard about a study which claims that the US is run by rich people? Well, the thing is, it's true, but not entirely. All classes are still capable of advancing an agenda. Louis Rossman can sit on a chair and yell into the microphone about right-to-repair[0] and get a bunch of state bills proposed. But rich people uniquely have veto power. They can, say, have a 'robust conversation' with a Senator or Representative to kill an R2R bill, or have New York State's governor change the R2R bill at the last minute to completely remove the legislative intent.

Filibusters are another veto mechanism; they raise the vote threshold from 50 to 60. Furthermore with the procedural filibuster they are significantly easier to use, so they get used all the time.

You know how Brexiteers were really mad about how the EU has a lot of unelected political appointees making law? They're not wrong about that. You see, whenever a political party in Germany, France, or the UK (pre-Brexit) wanted to push an unpopular policy, they'd make it into an EU-wide regulation and then blame the EU for it, because they think voters are stupid[1]. They were able to do this specifically because the EU works exactly like how the US Senate used to, with member state representatives not elected by the people and thus not accountable to them. And the only democratic accountability provided to stop this is to replace your member state's government with one that'll replace the appointee in the European Commission, which is now two levels of indirection.

Personally I'd rather live in the world with a straightforward democratic system with as little indirection as possible and few veto powers. Yes, you can point to rising populism as a counterargument, but the problem is that populism is rising because nobody's voice is getting heard. The more that the rich use their veto powers instead of relenting to the will of the majority, the more that the majority will turn to non-democratic means of power, and then we'll wind up in a dictatorship with exactly the kinds of people you don't want running things in office.

[0] Right to repair is a political campaign to undo several harmful effects of copyright and trade secrets law by explicitly requiring manufacturers to sell replacement parts and provide unlock codes to pair them onto equipment. It does not actually obligate them to repair the device, in fact that's counterproductive to the actual point, which is to restore ownership of your device (or car, or tractor) back to you.

[1] They're not.