Being successful (financially) is more important than winning in terms of hardware units.

I don't think there is a way they could have won this generation. Sony had way too much momentum going in this generation.  

But they could have set up a framework to be in a ridiculously strong position to win the next.

Start of the generation, or even slightly before, alot of people thought Xbox would be equal too or beat the PS5 in sales.
(I remember polls/threads here, and people were thinking it would be like neck and neck this gen)

Remember all that "it eats monsters, for breakfast" stuff?
(series S will compete in performance with the PS5, while the series X will be half a gen ahead in performance?)

There was a heavy PR and marketing push, and xbox commentators really hyping things up, and controlling the narrative on forums/youtube and such.
There was FUD (fear uncertainty and doubt) spread about the PS5, suggesting that it wasn't even really 10,2 Tflops of compute... somehow it was like 7 Tflops, and the overclock theoretical max performance would only be for limited games, when cpu wasn't used much.  Xbox side was shameless before gen started. (reality was clocks speed of the gpu, only goes up and down like ~2% depending on load, so its often close to that 10,2 Tflop performance level)

Yes, if Xbox actually did like a much much better job of things,... they could have done much better than they seemingly have.

Reality just didn't play out that way.

^ this.

early gen, or right before, it *felt* possible that they could have won the gen.

Yes, I don't see how Xbox could've won and I don't see it winning against PlayStation in the near future. Throw Nintendo into the mix and Xbox is a distant third place. Nintendo and Sony could basically have all future systems sell over 100m each whereas Xbox will likely struggle to hit 50m each future gen.

Yes, they could have won, they just had to care about their console.

Virtually unwinnable, terrible naming scheme, bad first party, PC focus etc. They're known more for cancelling games and shutting down studios then releasing great IP this gen.

Only if Nintendo never managed to turn a profit from the platform... Which ironically is probably hard to quantify over the long term as many of the Gamecubes best games are some of the best games of all time... And Nintendo has remastered/re-released them generation after generation and made money from those titles. I.E. Metroid Prime on Switch being a prime example.

Microsoft Series even though it's only sold a fraction of the Xbox 360 consoles, is still a success as Microsoft has made a profit on the platform. (Their gaming division since the Xbox Series Launched has raked in over $80 billion.)

I think this nails it. Series S|X were doomed to lose the race by much earlier decisions, but it could definitely have done better - so much better that we wouldn't need to ridicule it. There's no reason why Series S|X couldn't have done better than Xbox One, had better decisions been made, especially since Sony hasn't exactly been doing exceptionally well either (aside from sales, of course, but it's not been great in terms of exclusive releases).

I wouldn't count stuff like say Wind Waker HD or Metroid Prime Remastered as part of the Gamecube ecosystem personally, as by the time they were remade Gamecube was long dead and buried.

There's factors other than just profitability as well; Gamecube saw Nintendo's market share shrink significantly, which is not the mark of successful platform.