A true restoration should be the default strategy at this point unless someone can come up with a compelling design that is overwhelmingly beautiful. That may be impossible but it's a least a fun thought experiment. To my knowledge, Notre Dame in modern times remains an active participant in Parisian religious and civic activities. Historic but still at work. For that reason, I think it's worth considering how it can be renovated into the current image of the city, as cultural views on religion continue to change.
The tricky thing is it's already a sociologically fraught situation in that France's biggest luxury houses pledged 700m Euros to rebuild it. Rich people see this as trickle down economics. Not-rich people see this as proof that the rich need to be taxed more because, after all, it's not like they're giving 700m euros for hunger. Modernize Notre Dame and you're talking about memorializing a new Gilded Age which, frankly, will probably be a treasure 100 years from now but for the 90 years before that will be a divisive symbol of inequality.
Tricky indeed. I've worked on many public building designs. Community centers, recreation centers, libraries. One time my team was told that our proposal looked too good. The city did not want the perception that they were spending taxpayer funds frivolously. So instead of getting a building the town could perhaps be proud(er) of, they were given something not as good in my opinion. This is a different sitation though. It would be cool to watch a man-on-the-street type of interview to see how Notre Dame symbolically lives inside the minds of everyday Parisians.
I have been in it. It is itself beautiful and the space it creates in the city is incredible. I want to reiterate that I believe a potentially different idea added to the existing building is probably impossible to achieve because the original is just too powerful of an idea and image to manipulate and reenvision. Having it be the roof only is a constraint that even the best design can not overcome. In general though, I believe that it is ok to at least have a conversation about how a building can change for future generations. You're probably right in this case though and maybe the existing story of Notre Dame is in itself powerful enough to last another 500 years. What do you think it will it look like in 1000 years?