Bush 41, Bush 43, Clinton, and Obama all tried to rein in North Korea’s nuclear ambitions with a mixture of carrots and sticks. To that end, all of them attempted to pressure or persuade China to use its unique leverage with the regime. Unfortunately, all of them were unsuccessful. The North Korean threat did nothing but increase with time.
Trump tried a different approach: freewheeling personal diplomacy. In practice, this meant legitimizing Kim in exchange for a slowdown in the nuclear program. This approach ultimately didn’t work, either. The program still exists, with no end in site.
So what will Biden do? The legitimacy genie is already out of the bottle, so it can’t be used as a negotiating tool. My guess is that, under the new circumstances, Biden will have no objection to meeting with Kim, but that the element of unpredictability which existed under Trump will be removed. If any meetings take place, they will be preceded by the usual extensive staff groundwork.
In the end, probably none of it matters. The bottom line is that diplomatic and economic pressure don’t work with the North Koreans, and that the costs of a preemptive strike are prohibitive. Ultimately, we will have to live with a nuclear North Korea, and use standard deterrence principles to avoid war, if the regime remains (wrongly) convinced that the nuclear program is a guarantee of its survival.