You can read about how Edo Japan (or any period of Japan) was not feudal here and here.

But for the question itself: using the Tokugawa as an example: why didn't they just get rid of all the daimyō and rule via central administration? Why wouldn't any powerful king or emperor just get rid of all the local rulers and rule the entire country by central-appointed administration?

Alas, we can never for sure conclusively say why they didn't do something in history. But we can look at why they did what they did. And though bordering on hypothetical, perhaps we can get an answer why such a move likely wouldn't work.

First, the Tokugawa clan was no where as powerful as you imagine. According to the Jesuit report for Sekigahara, Ieyasu's contingent was 20,000 men. This was less than half of his combined allied forces, indeed quite likely less than a third. Now, for sure Ieyasu had to leave men to guard against the Uesugi in Aizu, and Hidetada's sizable contingent was late and would not arrive in time for the battle, so the total forces of the Tokugawa clan would be considerably larger. However, we must remember that the majority of these were not the forces of the Tokugawa family itself, but comprised of the forces of Ieyasu's vassals like the Ii and Honda.

If we go by Hideyoshi's and early Edo's land census information, then at the time of Sekigahara, Ieyasu's lands - including those held by his vassals - comprised of about 12% of Japan's agricultural production, and so by extension a similar amount of population and economy. This made him by far the largest daimyō, but it means that, numerically, there's no way Ieyasu could take on even a quarter of Japan by himself.

The agricultural production of the lands controlled by the ten men Hideyoshi left behind in charge is as below:

Daimyō	Koku (Thousands)
Tokugawa Ieyasu	2,560
Uesugi Kagekatsu	1,200
Mōri Terumoto	1,120
Maeda Toshiie	830
Ukita Hideie	570
Asano Nagamasa	220
Mashita Nagamori	220
Ishida Mitsunari	190
Natsuka Masaie	50
Maeda Gen'i	50

From this we can clearly see that, yes, Ieyasu was by far the most powerful, but he still needed allies. This is likely why Ieyasu backed down and agreed to leave central politics in 1598 at the confrontation in Maeda Toshiie's home. All other daimyōs aside, of the ten above it was nine against one. For 1600, Ieyasu had Maeda Toshinaga (Toshiie's son) and Asano Nagamasa on his side, meaning for the ten above he had rough parity. Even then, he was fighting under the Toyotomi name to weed out traitors (as was Ishida Mitsunari) and for the campaign had to heavily depend on Fukushima Masanori coming to his side and tipping the balance (likewise, Mitsunari was heavily counting on Masanori to come to his side).

It is of course true that the Tokugawa grew in power greatly following Sekigahara. But even at the height of Tokugawa power around the early 18th century, after a century of consolidation and confiscating domains (mainly from clans with no heirs that died out, the bakufu more often than not let the domains govern their locals independently), the Tokugawa's lands still made up less than a quarter of Japan's agricultural production, a third if we were to add in Tokugawa hatamoto. So, numerically speaking, there's simply no way the Tokugawa could take on the rest of Japan all by themselves. By extension, the Tokugawa also did not have the resources to directly govern all of Japan.

Of course, that does not mean they couldn't have created a central administration across the entirety of Japan, if enough other daimyōs supported the move, or at least agreed to it. That was what happened with the Meiji government, fresh from victory in the Boshin war, with a modernized army provided by Satsuma and Chōshū to intimidate the dissenting voices. Could Ieyasu, fresh from his victory at Sekigahara or Ōsaka, when he was far stronger and the Bakufu was on solid footing and the Toyotomi destroyed, have gotten enough support for the move?

Ieyasu was on his deathbed after his victory at Ōsaka, which would certainly have thrown a wrench into any such plans. And we, of course, could never know for sure, because he never tried. But we can examine some important differences between the early Edo and the early Meiji.

In the early Meiji, in the eyes of Japanese leaders there was a great threat of foreign colonizers, who simultaneously also provided examples for system of central administration and its benefits. Even then, the daimyōs were offered very generous stipends to get them to give up their domains to the central government. As well, the new government and its orders were dressed up with the emperor's legitimacy, and it used terminologies, like name of bureaus, titles, political vocabulary, that were reminiscent of the Heian court's centralized administration. And of course the entire bakumatsu movement was done in the name of restoring the emperor's (direct) rule over the country. And the warriors themselves have spent two centuries as bureaucrat administrators, being taught Neo-Confucian ideals and complete loyalty to their domain.

None of these factors were the same in the early Edo. There was no threat of foreign invasion (in fact, the Spanish were afraid a united Japan would invade the Philippines). There was no good example of central administration worth copying (Chinese central administration was also fairly minimalists, and given how the Heian turned out its unlikely any daimyō thought it a good idea to return to that system). Ieyasu was not of the imperial family or of Kyōto's aristocrats. He was from a warrior family, and naturally chose to set up a bakufu like the warrior rulers before him. And of course after Sekigahara, he was nominally still a Toyotomi vassal, and he had to support the aristocrats taking back the position of imperial regent to get their support for founding the bakufu, and they certainly would not have been very happy if he went to remove that title after Ōsaka. And of course, all the warriors, including Ieyasu himself, were brought up in the chronic-backstabbing civil war of the Sengoku where it was every man for himself, where everyone did everything they could to better himself, which means get more land, leading Jesuit Luis Frois to comment that treason in Japan was so common no one thought it was dishonourable. This culture of course extended into the early Edo, when even though there was no wars there were still a lot of people trying to grain or regain land through back-room dealings (and the Tokugawa was arguably one of them). Given that then, there was no reason why the Tokugawa would want to set up a system of central administration. Even if they did, they had no legitimacy to do so. And even if they did have the legitimacy as well, they likely would not have been supported by the other daimyōs. And they must have remembered the examples of the Oda and the Toyotomi: one wrong move and your entire regime could come crashing down in a few short years.

So in summary, the early Edo Tokugawa had not the motivation, the legitimacy, or support for such a move. Unsurprisingly, the Tokugawa instead did what they had precedence for and which they thought would get them more political power: set up a Tokugawa woman as empress. Even that caused enough of a political stench that the third Shōgun Iemitsu backed off from further encroachment with the court to repair relations.

Finally, we need to note that the political system the Edo bakufu set up gave the bakufu considerably more power than the feudal kings of Medieval Europe. All daimyōs alternated their time between Edo and their own domains, and all had their wives and families in Edo as hostages, all domains had to submit census information, help run the country, follow Edo's country-wide laws, mobilized troops to support Edo in a systematic-conscription fashion, and otherwise go out of their way to acknowledge Edo's superiority. In many ways therefore, the Edo bakufu, even if it left the domains to run their own local affairs, had power over Japan no less than that of the court of Europe's "absolute" monarchs of the time. In some ways, Edo might even have had more.