The idea that Japan's entire transportation network goes into meltdown when the cherry trees turn pink appears to have become a significant trope on English-speaking social media. While it's true that some locations (e.g. in parks in Tokyo) will get crowded, some hotels in areas that are famous for cherry blossoms will get booked up in advance, and some scenic roads will fill up with traffic, I think you can rely on Japan's busiest airport to handle the flow of people as well as it does on any Saturday that isn't the start of a three-day weekend, or Golden Week, or Obon, or the New Years holiday. Those are peak travel times. An afternoon when tipsy crowds hang out under the trees in Ueno park is not going to cause a meltdown at HND.
That said, there's nothing wrong with the advice to allow three hours for a less than nail-biting connection.