That was the magic of Season 3?
So yes, a good part of "the magic" of Season 3 was the last ride of the TNG crew. Absolutely.
However, it wasn't the only thing. There was also perhaps a more accurately labelled "magic" that is harder to define in that Picard S3 "felt" more like Star Trek than much of what has come of the new era. That was NOT because of the TNG crew.
Picard S3 actually felt like a continuation of Star Trek. Not an update, not a reimaging, not a "visual update", not a Trek in spirit, not a "new direction". It felt like a modern continuation of the TNG/DS9/VOY world that so many of us enjoy.
For Legacy to be successful, no it couldn't rely on doing what S3 did. That was always going to be a one-shot. It CAN, and SHOULD have some sprinkled in... there's no reason Admiral Riker wouldn't show up from time to time, or for Commodore La Forge to show up on occasion. I would probably sprinkle them somewhat conservatively, but absolutely exist.
Legacy could scratch the itch that Prodigy and Lower Decks do in part... many Star Trek fans want something that is a continuation of the world we like. I'm all about new stories and new ideas... of course. I want that. I want those new stories and new ideas, set in the world of Star Trek that I like.
People are different, but when I like something, I tend to like all (or most) of it. I don't like Star Trek because it's in space and there are ships and people doing stuff in space. That's a part of it. I also like the "stuff" of Star Trek. I want to see Star Trek ships that look like Star Trek ships because that's what I like. I want to see things familiar to the world because that's the world I like.
I don't know people seem to have some mental block that prevents "new ideas" from occurring in the established universe. You can do both. It's actually not that hard.
I can equate it to something else. I'm a huge Ghostbusters fan. The "magic" of Ghostbusters are very much the original 4 guys. However... I also very much enjoy the two newer movies. The original guys were there, sans Harold Ramis. The "world" was clearly the same. It was a continuation of the thing I like, clearly set in the same world with the same things, but new stories that also had new characters and situations.
That's what I want.