I guess with United there's also the sentimental argument. When I think RVP, I think of him as a United legend and almost forget he played for Arsenal. If Kane joined and spearheaded us to the title or a big trophy, he'd be adored at United just as much.
There's also the draw of United that you can't ignore. Look at the players we've signed even when we've been useless for the past decade. Antony, Sancho, Casemiro, Varane, Martinez, Bruno in recent times alone.. plenty others too that I could list. I don't mean this in an offensive way, but Spurs would never be a choice ahead of United for any of them. There's still an unmistakable draw to play for United.
Now whether that makes any difference for Kane, who knows. But he's not going to Arsenal or Chelsea, Liverpool have spent big up top and he won't spend the last few years of his prime competing with Alvarez and Haaland at City. Barca have Lewandowski and Madrid still have eyes for Mbappe. That leaves Bayern and PSG, but I just can't see Kane in France or Germany, even though both guarantee trophies and a good shot at the CL.
I guess it's just a question on how much does he value Shearer's record. Of course, he'll probably still break it playing for Spurs, so you do have a point that there's no clear reason why he'd join United. If he values winning something, then moving abroad to a top team is the clear option: he keeps his Spurs legacy relatively untainted and win something. If he wants the all time PL record, he could very well stay at Spurs. But I wouldn't be one bit surprised to see him join United either, because we still have that draw for top players... the history, the sentiment, something extra.
Put Kane up top at United and I think we could compete for the league with no other signings. Spurs still need, to steal Rangnick's words here, open heart surgery on what's a very average team without Kane, to compete.