I haven't heard from Frogger, Bubble Bobble, Dig-Dug or even Bomberman in awhile, so maybe Sega thinks there's no need to compete against them. Especially with Puyo Puyo as their top puzzler.
Frogger, Bubble Bobble, Dig-Dug, and Bomberman are rarely considered as puzzle games.
They're usually placed into arcade action genre.
Puzzle games usually are with gameplay that's more like Tile-Matching, Logic-and-Deduction, Point-and-Click, Escape Room, or Hidden Object.
Example for Tile-Matching puzzles are Tetris, Columns, Soldam, Bejeweled, Magical Drop, and of course Puyo Puyo.



Chuchu Rocket series somehow was considered as puzzle because we didn't directly control the mice (unlike Frogger, Pac-Man, or Bomberman where we controlthe character).
We control the placement of arrow buttons instead.

The DS games really need a re-release.
I already played them a lot back then till the point I grew bored of them.
But still love to hear their soundtrack though, especially this one:
https://www.youtube.com/watch?v=LZjBjYOpxG8