Is he as important to the franch as Meta or DDD? Don't get me wrong, to me he always seemed like that sidekick no one asked for.
*sigh*
Guess I gotta do it to 'em.
Bandana Dee first appeared in Super Star as the first opponent of Megaton Punch. A very small role, but a very early start nonetheless.
Following this, Bandana Dee received an upgrade in Super Star Ultra, where he gained a speaking role as Dedede's right-hand-man. He also was present as the only audience member during the Masked Dedede fight.
Bandana Dee's role really starts to take off in the period after Super Smash Bros Brawl. Keep in mind that since Brawl, Bandana Dee has actually had more appearances than Meta Knight. Yes, he's that important.
Bandana Dee's first playable role was in Return to Dreamland. He immediately sets himself apart from other Waddle Dees as the only one capable of wielding the Spear moveset. In addition, he appears in all of the cutscenes and is viewed as part of the core cast of 4 characters.
Following this, Bandana Dee took a support role in both Kirby: Triple Deluxe and Kirby: Planet Robobot.
Between these two titles, Bandana Dee had another playable role in Kirby and the Rainbow Curse. In this game, Bandana Dee is the ONLY playable character other than Kirby, putting much more of a spotlight on him.
Then we come to the 3DS e-shop titles, Clash Deluxe and Battle Royale. In one, Bandana Dee has another speaking role as a voice of friendly advice in the hub. In the other, Bandana Dee has a speaking role, AND is your in-game partner. He is cemented as Kirby's best friend and gains his own distinctly-colored parasol in addition to his Spear, which he is still the only user of.
Cut to Star Allies, where Bandana Dee is the ONLY Dream Friend available at the start of the game, essentially the de-facto Player 2 character. In addition to this, with the removal of the Spear ability, Bandana Dee's moveset is now entirely unique to the cast. In one of the extra Puzzles that can be assembled, Kirby and Bandana Dee take center stage at the Fountain of Dreams, while Meta Knight and King Dedede are relegated to the background.
Combine all of this with Bandana Dee constantly appearing in group shots with the other 3 core cast members, and it's inarguable that he's distinguished himself as a core member of the cast with his own unique skillset and personality.
Find me a Goomba that does that.