The problem with that would be, Is Hideyoshi really going to risk throwing the entire Japanese political order out wack like that, and risk what is essentially political suicide? If accepting being king of Japan means doing away with the emperor, Hideyoshi has seemingly all but ensured that Japan will fall to chaos if he mismanages his succession. You at least had The Shogunate system to maintain a semblance of order even if it that relied on actual force to back that up, and Hideyoshi still needs military force on his side and Ieyasu still has the Kanto plain. This is an insanely risky gambit to pull off.
Hideyoshi is at risk of being branded a traitor in a magnitude that would make Saito Dosan, Matsunaga Hisahide, and even Akechi Mitsuhide seem loyal. Hell this could play right into his enemies hands, especially if this pisses off the Daimyo he sent to Korea. It would be a massive political coup to Ieyasu as instead of just winning out, he would be known as the man who "saved" Japan if Ieyasu can gain power with the shadow of Sekigahara we could conversely see a longer Tokugawa Shogunate with that kind of goodwill and a less shaky start position.
Oh, that's certainly true. I alluded to it above, though in a bit of an understatement:
some internal unrest seems a bit likely either way
Now, I'm not sure that 'being king of Japan' necessarily meant 'doing away with the emperor,' since the emperor still remained a figurehead at the time and nothing much would've changed in any meaningful sense in terms of that order (could pay homage to two emperors instead of one, if the Ming's terms allowed for that and that requires knowing more specific details about what peace was offered) but the idea of Hideyoshi gaining legitimacy to rule from an erstwhile enemy probably wouldn't be too palatable for Toyotomi opponents.
As for mismanagement of succession from the Toyotomi clan, well...hindsight is etc. etc.
In any case, there was no chance of the Japanese taking that peace deal while they were still under the impression they could 1. win the war and 2. the Ming wouldn't be able to force their submission. Which, seeing how badly the Joseon muddled up the Imjin War prior to Ming intervention, would require either the Japanese to lose ground prior to Ming intervention or for the Ming to push the Japanese all the way back to the Korea Strait, which itself requires having one of the most brilliant militaries in the world or having ideal logistics (both of which are not gonna happen during the war).
One idea I was mulling over that could've gotten the Japanese to at least consider the offer was Jurchen involvement in the war. Turns out Nurhaci (yes, that Nurhaci, the who pummeled the Ming in the 1600s) of the Jianzhou Jurchens offered to aid the Joseon against the Japanese (the Japanese had attacked the Jianzhou on a side expedition in their time in northern Korea, the Jianzhou were concerned with future conflicts as the previous one was more or less unprovoked, Nurhaci wanted to get favour with the Ming court, and Nurhaci wanted the military details of the Joseon and Ming forces in order to better prepare himself for the future) and spent a fair bit of effort trying to cozy up to the Ming and Joseon in the process (while the Ming were receptive to the help, the Joseon turned him down out of concerns the Jurchen would pull a Uighur on them and sack Korea after driving out the Japanese). Say, if King Seongjo were to die during the war, the Joseon court was in disarray, young King Gwanghaegun the pragmatist in power a decade and a half early, then that might not be too unlikely a change.
Seeing how quickly the Japanese withdrew back from Pyongyang back to the middle of the peninsula after the Ming sent 40,000 men to fight, it got me wondering what would've happened if the Jurchen had joined the war with its full force prior to Ming involvement. If the Japanese are still pushed back and then the Ming got involved to break a potential stalemate, then the peace negotiations would take on a decidedly...well, Toyotomi Hideyoshi wouldn't be expecting to receive half of the Korean peninsula and be surprised with none of it in that case.
Though that also creates massive butterflies elsewhere, with the Joseon being more ambivalent or even friendly with the Jurchen/Manchu going forward and possibly butterflying the two Manchu invasions of Korea, the speed at which the Jianzhou consolidated power in Manchuria (war with Japan means less focus on uniting the Jurchen tribes), and the decline of the Ming in general (while it doesn't get rid of all of the causes of Ming decline, like the emperors' incompetence and paranoia, a slower Manchu unification means less military pressure on the Ming's northern border and that in itself cascades into a very different East Asia in the 17th century onwards).
But yeah, that's just one idea (and a timeline I might get to someday) for changing Japan's political destiny in that manner.