I think House Republicans are walking a very thin line here. They know rushing ahead with this impeachment or any against Biden risks a backlash in next year's election because people are mostly smart enough to tell when something is being done legitimately as opposed to being political brinkmanship. As such they have to slow roll this and at least put on the appearance of doing due diligence.
But secretly even the "cooler heads" like McCarthy (who publicly urged his conference to vote against it) want this and other impeachments against Biden to go through. And it's not because they even believe he did anything wrong. It's because they know full well that Trump or DeSantis or whoever the next GOP President might be will be committing many impeachable offenses as a matter of course. And if Democrats control the House then they will submit articles of impeachment. That was certainly damaging to Trump during the previous term and they don't want it to happen to them again.
They want to break rules without facing consequences. And the best way to do that is to simply trivialize the act of impeachment itself, to make it a game. Now every President will get impeached a couple times as a matter of course. It's not an indicator of anything serious anymore, it's just part of your regularly scheduled political theater. Republicans don't want to impeach Biden to break the Biden administration. They want to impeach Biden to delegitimize the impeachment process itself.