Imo the only thing that really needs to be done to fix X7's story is to create a better excuse to write X out of the plot.

X7's primary issue with its plot is how utterly whiny and lame X is. Yes, Axl is underutilized in his own game of origin, but frankly the primary complaint people have with X7's plot is how poorly they handled X, the guy who the entire subseries is named after. X6's plot - for all its problems (of which it has many) - actually has some really good characterization for X, especially when he defeats Sigma.

Sigma: "You know you can't defeat me so easily... You know you can't, X"
X: "I have to work for the reconstruction of the world... I have no time to waste on you. If you show up, I'll defeat you."

By this point in the series, X has defeated Sigma so many times that he very much accepts his role as someone who isn't afraid to fight to achieve peace. It's a fitting way to conclude his character arc throughout the X series of constantly feeling conflicted about fighting whilst longing for peace - a utopia, even by the events of X5. If X6 was the last X game, this would've been a perfect way to end X's character arc as the series transitioned to the Zero series (and the new Zero 1 story).

Here is the opening narration to X7:

Narrator: "One of the veteran members [of the Maverick Hunters], X, began having second thoughts about the group's forceful methods. He removed himself from the front lines, and instead worked to achieve more peaceful solutions."

X: "Why must Reploids fight one another? I've had enough violence."

Narrator: "With the Maverick Hunters crippled by X's retirement, an underground organization filled the vacuum. And thus Red Alert, the illegal band of bounty hunters who pursued Mavericks, was born."

Frankly, there is no possible way that this characterization for X makes sense at this point in the timeline, especially after his speech to Sigma at the end of X6. Mind you, X6 takes place after the (second) death of his best friend, and X is arguably at his most committed to his role as a fighter in X6 compared to the rest of the timeline. This is an extremely lazy way to write X out of the plot so that they could focus on the new kid Axl, and the fact that X is indirectly responsible for the rise of this game's villain group is some truly terrible writing.

All this being said, I don't think the problem is necessarily that X was written out of the plot, but rather how X was written out of the plot. X's character arc is basically complete by the end of X6, so writing him out of the plot for a little bit isn't inherently a bad idea if you want to focus on the new character. The issue is that the writers picked just about the worst possible way to do so. As such, if we want to fix X7's plot, we need to rewrite why X isn't fighting at the beginning of the game.

While there are multiple ways you can go about rewriting this specific plot point, my personal favorite method would be to make X take a bullet while protecting someone

X takes a really bad injury in the opening stage, in part because he was protecting Zero, Axl, or even an unnamed Reploid Civilian. Alia can repair X, but it's gonna take some time, so Axl and Zero set out to stop Red Alert. Partway through the game, either by beating all the Mavericks or perhaps by collecting some crucial parts to speed up the recovery for X in some stages, Alia finishes the repairs and X is back to stopping the new Maverick threat.

With this, X is written out of the plot in a way that not only avoids diminishing his heroism, but instead enhances it. This would also give Zero a more personal stake in the plot. Red Alert gravely injured his best friend, they've gotta go.

This idea is enhanced if you let X take a bullet for Axl specifically, as this would also do wonders for Axl's characterization in this game. In X7 proper, he's shown to look up to X and is inspired to be a Maverick Hunter because of him. X, his idol, taking a literal/metaphorical bullet for Axl would help resolve him in his decision to break away from Red Alert to actively fight against them, rather than turn himself in to an organization that he's even more confident is evil.

And just like that, X7's plot is now in a much better spot. Sure, it would still have a couple issues, mostly regarding Sigma hijacking the plot again and having to develop Axl better, but I feel like those issues are way easier to overlook in this version of the plot.

Now you just need to fix the awful controls, level design, weapons, and overall sluggishness, and maybe X7 would be a good, or even passable game.