Harry is the patron of Invictus. What does this mean? Harry is not a "Royal Patron", since he no longer represents the RF or Britain. If a RF member is a patron, the Sovereign grant covers their expenses, and the the patronage is purely to bring attention and donations. The RF also has the Royal Foundation to support their patronages directly. The RF might still contribute to Invictus, but it is not because Harry is a patron.
For a non-royal patron, I found several sources like this article saying a patron "generally refers to well known or illustrious individuals who lend their name and support to the organisation, who may or may not have membership rights.’ The role is spelled out by the charity, but the underlying purpose is to raise the positive profile of the organization, thus increasing support and donations.
The article warns about the "cons" of having a patron. Two that apply to Haz are:
o The patron may lose some of their value (i.e. celebrity status fades, political contacts go stale etc.); and
o The patron becomes a liability (negative press, involvement in scandal and so on).
So with "just Harry" we have a high-profile former Royal, whose bitterness towards the Royal family is repeatedly brought up in interviews, articles, Netflix show, and of course his "bestselling" tell-all book. Now he's being sued by another charity, his popularity has faded, and he remains a huge thorn in the side of the King and Prince & Princess of Wales. He has lost the public's confidence, which has led to investigations into the games' budget like Kiwi's. And what's more, participating countries are going to be worry where their money is going. I think Harry has crossed the line into into being a liability, and should be removed.
Now, if Harry were donating all of his time, and defraying his own expenses (as well as his wife's if she attends) and attracting lots of positive press and big donations, it would be a different matter. But it appears Invictus pays for Harry's luxury travel/ and accommodations, expenses galore, publicity, travel to Australia and Ukraine just to embarrass himself, probably a full time staff person (based on Kiwi's great analysis), all the while pretending to be a war hero by accepting awards ("legend of aviation??") despite being Bunker Harry and not being able to fly a helicopter alone. To me this is scandalous.
Moreover, the Invictus "Patron" is using the games to try to prop up his own fading reputation. Let's be clear: Harry would be nothing and nobody without the Invictus games. That's not the role of the Games - they are to help wounded veterans, not make dim Harry appear to appear heroic.
The veterans deserve more than having a charity dedicated to them used by an unpopular "patron" to appear to be exactly what Queen Elizabeth II said is unacceptable: a half-in, half-out "Royal."