The stories I have heard thus far about Genie+'s effect on the standby lines and what others have been able to do with it if they do want it have given me some hope. Like
@CaptinEO said, it will fully depend on how many people buy it up on any given day.
But I'll say this, in the two days I spent there this month (3rd and 4th, just before Genie went live), we hardly waited for anything (other than RotR and an extended queue for our dinner selection). We rode over 30 attractions within the two days we were there and on average, their wait times were about 20 to 25 minutes each. The reservation system plus lack of any sort of Fastpass really made the day feel enjoyable, manageable and had a liberating degree of freedom involved. If we wanted to do something, we just did it without having to worry about any sort of return times or fear of super long waits.
Hopefully, given the reality I experienced, maybe less people feel the need to shell out the extra cash for the Lightning Lane options. Sure, it leads to an expeditated experience overall but if the difference between shelling out an extra $60 for a party of 4 is only 15 to 20 minutes more of a wait per attraction, then I could totally see why less people would feel the need to spring for the upcharge. If things remain the way they've been for the foreseeable future, then I certainly won't need to. My last experience was awesome.
I also remain hopeful this to be the case because I know how booked the Magic Keys are at Disneyland right now. The maximum amount of allowed Magic Key holders are currently in the park each day and I believe these to be fans who are "in the know" enough to know that Genie+ is live and available to them.
@CaptinEO's experience leads me to hope that this isn't actually a matter of dreading when more people will figure it out. Maybe, just maybe, the controlled crowd levels and lack of free Fastpass will be enough to keep wait times and crowd levels at a level enjoyable enough that most Guests will decide they don't even need the Lightning Lane to begin with to get the most out of their day.