Why are the GOP pursuing Biden ?
It sems to be a waste of time. They could be telling us about their exciting policies.
It's good to ask questions of the American system. I think there are aspects that we've always known that an outside observer might not.
Unlike in your Parliamentary system, in our Presidential system, the Chief Executive is separate from the legislature, meaning among other things he's not part of a group who can remove him. Realizing that, plus the fact that he does not operate in the name of a monarch, the Founding Fathers debated what to do if a President commits a crime. The answer they had was impeachment.
Impeachment isn't a legal process, it is a political one. In our legal system, a Grand Jury of 25 people decides if there is enough evidence for a full case; for the President, the 435-member House of Representatives decides this as their "impeachment." The trial is held by the 100-member Senate, with the Chief Justice acting as judge, but instead of deciding guilty or not guilty, they decide whether or not to remove him from office.
Because he is under no risk of imprisonment or anything worse than losing his job, he can't claim any of his 4th, 5th, 6th, or 8th Amendment Constitutional rights; it's all purely political, governed only by House and Senate rules. He doesn't even need to have committed a Criminal Code offense; for example, Nixon and Trump were both charged with "abuse of power," which isn't an actual crime. The Constitution specifies that impeachment is for "treason, bribery, or other high crimes and misdemeanors," but it didn't define what that included specifically; it's basically entirely up to the House.
Impeachment also applies to federal judges and members of the Cabinet, and over the years more than a dozen have been impeached. Of the Presidents, Andrew Johnson was impeached in the 1860s, then Bill Clinton in the 1990s, then Donald Trump twice. (The House wrote up Articles of Impeachment for Richard Nixon in the 1970s, but he saw the writing on the wall and resigned before the House could vote.) The decisions to remove in the Senate were right down party lines for Johnson and Clinton, but Trump got a few of his own party to vote for his removal.
The Constitution doesn't outright say "The President can't be arrested," but we've operated under that assumption ever since. In essence, that means the President can't be arrested ... under federal charges. Because we are fifty separate political states operating together rather than one big monolith split into fifty parts, the States can theoretically bring their own charges against a President, though in practice I think that wouldn't be pursued, for national security if nothing else.
All of that boils down to this: The President can't be arrested, but he can be politically impeached. That would sidestep all of the burdens of proof and standards of procedure that the pro-Trump wing has not had much luck meeting. It would also be a black mark against Biden even if he wasn't removed, and being able to say "See? Biden is no better!" would give the pro-Trumpers reason to diminish the sting of Trump's own impeachments. So it's an obvious political target, but that's what it is: a political thing.
It's not a perfect system.