I don't really see how Splatoon 3 could've reached a bigger audience.
With all due respect, that not for you to figure out, it's Nintendo's job to try to better themselves.
With that being said, I see two pathways to grow the audience of an already successful IP.
1. You keep the same core, but do everything SO MUCH better that the game becomes as close as it gets to perfection. That's Mario Kart 8 deluxe, that's Smash Brothers, that's Animal Crossing (though I haven't played the latest). For Splatoon 3, top of my head, that would have meant much better designed arenas, a much tighter netcode, a much lower controller latency. In the end, I'd argue that most of the new arenas are actually worse than Splat1 and 2, and the game is still largely latency-ville featuring double splats-festa. There was room for improvement and Nintendo partly failed at that. The new mobility options are great, I give them that.
2. You reinvent yourself without betraying your IP's identity. This is what Zelda did, and it pays dividends. It's very hard though, but after a sequel as incremental as splat 2, for reasons which were perfectly understandable, one was allowed to expect a less risk adverse Nintendo with splat 3.
(Edit: 3. Obviously, a combination of 1 and 2. )
As Splatoon 3 failed at both point 1 and 2, it's normal that the audience didn't really grow. And to speak for myself, I'd also find normal if people felt less involved in splat 3 than they did in 2. I know that I haven't touched the game in months, even though I was playing splat2 until 2020-ish. The game is still good and polished, and the core concept is great. But it's a 10/10 game weighed down to 8 by the aforementioned problems, in my opinion.
As Nintendo didn't have new ideas justifying the sequel, nor the time/money/manpower/interest/ability to make Splatoon 3 perfect game like MKDX8 is, I would have indeed preferred if they made Spin off rather than a sequel; everyone would have been ok if they just updated Splat 2 for another couple of years. Actually, most of us expected exactly that.
After all, we are talking about the company which refuses to make a new F-zero for their lack of ideas in how to rejuvenate the IP; I totally understand that the case of Splatoon is different due to $$ involved, but I wish they kept that same energy.