There are multiple answers.
A) Trump knows full well there's no legal way to do this, therefore, he's outsourcing to Ukraine, a country he knows is laden with questionable people and Russian connections. He hired Manafort, for example.
B) Trump isn't groveling, he's extorting, because he knows no honest country wants to touch this. Other countries
liked Obama/Biden. They don't like Trump.
C) Trump isn't groveling as much as he is making a deal in a back alley. You don't just walk into a shop and say "one drugs, please". Same here. You don't just pick up the phone and say "Investigate my political rival". I mean, apparently you do, but then you realize how bad that sounds and you hide that shit in a safe.
D) The obvious one: Trump needs his rabid fanbase to look at him as the underdog, the oppressed, the scrappy little guy who pushes around the big guy. Obviously that's bullshit, he inherited yuge bigly gobs of cash and used it to hire lawyers to prevent people who sued him from getting their wages. But his narrative "they won't let me" only works if he doesn't do it. He doesn't even just use it on "the Democrats" he uses it on everyone. "
I wanted to fly to see you guys, they said the weather was too bad, and I didn't have a Sharpie" when he canceled a flight because of the rain...well,
half the time, anyhow.
Exactly how Trump will claim "they won't let me" investigate Biden when his personal lawyer Barr is the head of the DoJ is beyond me, but he's working towards it now. "Oh, the Democrats, they've stopped me from investigating Biden over a thousand days into my tenure, just because they caught me doing it illegally. LOST THEIR MINDS? COVFEFE?"