The rules in Heroic Inspiration state this:

If you (a player character) have Heroic Inspiration, you can expend it to reroll any die immediately after rolling it, and you must use the new roll.

If you gain Heroic Inspiration but already have it, it’s lost unless you give it to a player character who lacks it.

The rules on Percentage Chances state this:

Sometimes you might see a rule describing a percentage chance of something happening. For example, a rule might say there is a 5 percent chance of something happening. You can determine whether that thing happens by rolling percentile dice; if the roll is equal to or less than the percentage chance (a 01 to 05, in this example), it happens.

Does that mean I can reroll a percentage chance using Heroic Inspiration?

Yes. You can reroll any die using Heroic Inspiration, including percentile dice rolled for percentage chances of something.

However, keep in mind that Heroic Inspiration can only be used on dice you roll, not on dice the DM rolls for something that affects you.

RAW, who would roll the chance to never be able to cast Wish again?

There's no RAW answer because the rules don't define who rolls an ambiguous percentage chance as it's worded in the spell. That'd be something to discuss with your DM