The Tokugawa shogunate was not all that centralized. The Shogun himself held little actual power or influence....
The Tokugawa Shogunate was many things; great centralization of power was not one of them.
I'm not entirely certain why this has become the topic of discussion of this thread, but I will reply to say it's a matter of degrees. The Tokugawa system was a feudal system that was more centralized than the Imperial system that came before it. The Shogunate government levied control over the daimyo through koku taxes, hostage taking, and demands that daimyo spend half the year in Edo (reducing their finances).
Was this totalitarian, centralized government? No. As you both point out, the daimyo had some amount of freedom to do as they needed. Especially in the larger states of Choshu and Satsuma, which over time became economically well off. But make no mistake - those who challenged the early Shogunate government had a nasty habit of being dead, and the daimyo were well aware where that line was.
It wasn't until 250 years after the establishment of the Tokugawa Shogunate that a series of weak Shoguns and confrontation with the West caused the Shogunate to loosen the strings on the daimyo, including relieving them of their duty to spend time in Edo. The more well off daimyo were even consulted by Shogunate government, and with the restraints lifted on voicing their opinions, rebellion by the more economically powerful daimyo soon followed.
Prior to the bakufu's collapse, it was fairly centralized for a pre-Modern state. But to claim, as some have, that the Meiji restoration gave uncannily centralized authority to the Emperor is a fallacy. The Meiji government was only by degrees more centralized than the bakufu had been when it was strong, and the Emperor remained as largely a figurehead of a constitutional monarchy.
In terms of ability to modernize the Japanese state, however, the Meiji government was astonishingly effective and efficient. More centralized? Not really. More competent? Absolutely.