It could one day become that important, but let's face it, a large part of the race's original appeal was its throwback nature. It was deliberately created to be a throwback to those racing days when those were the races. It will take plenty of time to the point where the Sagans and Cancellaras of this world are classics superstars of yesteryear in the way that de Vlaeminck et al are now, and that its origins as a wilful throwback are obscured as it becomes a traditional part of the calendar, and then it might get to that level.
I still think it will fall short of MSR and Lombardia, but it can probably eclipse the other non-monument Classics because it offers something distinctly different. Remember, plenty of very strong races have joined the calendar between the inception of the 5 races now known as the monuments and have become established high profile classics without being worth more than them - Amstel Gold Race (1966), E3 Prijs (1958), Gent-Wevelgem (1934), Omloop (1945) for example - and the fact that, unlike most other such one-day races Strade Bianche offers something unique, which is something that the Monuments all have in their favour, is a major weapon in its arsenal for future acceptance. Let's remember there have been lots of "sixth monument" type races over the years - Flèche Wallonne, Paris-Tours, Züri-Metzgete - which have fluctuated in prestige as time has gone by. As things stand Strade Bianche is, ironically enough considering it was created to be a throwback, a "modern classic" or an "instant classic", but not yet something in which the prestige level with the Monuments is considered inherent, and while the calendar spot is part of that, the fact that we do not yet have a generation of cyclists who will have grown up with winning Strade Bianche as one of their dreams is part of that. In the days when the young prospects grow up idolizing Cancellara and Sagan and their like, perhaps that will happen, but right now the race simply cannot have that, simply as it didn't exist when the current péloton were children dreaming of success. They will have grown up dreaming of mimicking the achievements of de Vlaeminck, Kelly, Argentin, Moser. When we have a generation for whom Cancellara, Sagan, van Avermaet etc. are historic precedent in the same way as that, things may change and Strade Bianche will join the top tier of prestige, but not before.