I have here in WDW since last Thursday and when I buy
Genie+ it is usually the morning of my visit right before booking starts at 7. I have never not been able to purchase it, so I don’t think that is really an issue.
But that's because, until this point, Disney has not capped Genie+ sales. Until now, they had made it clear that Genie+ never sells out, and anyone who wants to give them $15 can have it. The big change here is that Disney is now saying that they will limit Genie+ sales, like they do with ILL$ sales, and if you don't act fast enough, you may be shut out.
We don't know whether the cap will be so high that it will only sell out on the very busiest days. Disney had doubled down on their tempered expectations language -- "We expect that, on average, guests who purchase Disney Genie+ service will continue to enter 2-3 attractions or experiences each day using the
Lightning Lane entrance when the first selection is made early in the day." That suggests that sell-outs will be rare.
But perhaps Disney is just being cautious at this point.
They wouldn't be making this change if they didn't expect to sell out sometimes. And I suspect they are thinking about (and perhaps will experiment with) a significant cap that will come into play on many days. That would greatly enhance the value of the product.
If so, one imagines that Disney will increase the price enough to make up for the decreased volume of sales.
But we know that Disney doesn't price these things at the maximum amount that the market will bear. The fact that ILL$ for FoP and RotR sells out in minutes almost every day tells us that Disney could charge a lot more than they do. But for whatever reason, they have decided not to. I suspect it will be similar with Genie+. We will see a price hike, but not one that maximizes supply/demand utility.
And therefore, it will sell out quite often. Now will it sell out before 7:00 a.m.? If so, I suspect that Disney will stop opening sales at midnight, and switch to 6:30 a.m. or something, in order to avoid putting people in the untenable position of having to stay up late every night and wake up early every morning.