Senate rules currently require the chamber to hold a trial once the president is impeached. McConnell himself has cited them as reason for why he can’t simply toss the articles of impeachment in the trash once Pelosi delivers them. In reality, he would want to hold a trial anyway for the simple reason that it helps vulnerable Republican incumbents like Cory Gardner, Martha McSally, and Susan Collins to show voters back home that they’re taking the case against Trump seriously before they inevitably vote to acquit. They’re going to try to soften the political blow by doing the same "prayerful" shtick about their deliberations as Pelosi did for hers. No need to make voters on the other side any angrier than they’re destined to be by appearing arrogant and contemptuous of the Democrats’ allegations against Trump.
Hawley doesn’t care about that, though. His seat is safe-ish in Missouri and he has his eye on the White House. He’ll be as contemptuous of the House effort as he can be in order to make an impression on Trump fans even though his proposed resolution to change the rules would obviously be an uncomfortable vote for Gardner, McSally, and Collins. The base wants to see Pelosi punished for impeaching the president and for her dopey delay strategy in refusing to send over the articles. What better way to do that than to change the rules to empower the Senate to dismiss impeachment if it isn’t brought in a timely manner? Federal courts allow it in criminal cases. Why should impeachment be different?