The range of those 16 inch rifles was about 20 miles or so, not 100. And as accurate as they were they'd never be able to hit an incoming missile moving at Mach 7 unless it was the luckiest shot in history.
Range and max alittued are not the same thing. However I suspect you are correct in that her shells could not reach 100 miles altitude.
As to being able to hit something anywhere near that far away, it would depend on the nature of the "shell". If it was mostly second stage and guidance, (don't need anywhere near that much warhead to kill an ICBM RV) it might be able to achieve both the range/altitude and be able to hit the target.
I wonder though... What about a sub-calibre round? If it can toss 2700 lbs 20 miles, how high could it put say a 200 lb kill vehicle? If it could get it exo-atmospheric and reasonably close, then the kill vehicle merely has to manuever into the path of the inbound. Kinetic engery does the rest. Have to maybe run the numbers and see if it is feasible. Of course, that assumes you can build a 200 lb kill vehicle that can survive the tremendous acceleration being shot out of the barrel. The Navy does have ERGMs which sort-of proves the concept. (or disproves it, depending on your take on ERGMs) Another problem may simply be what is the max elevation the 16ers can be fired at? Would it even be realistic to get a projectile exo-atmospheric?
I like the old BBs, but sadly there's not much of mission left for them.
Your information is 20 years outdated. At least. In the 90’s before these ships were decommissioned again, tests were conducted using 115 mile range guided 11-inch sabot rounds. This was part of the first Gulf War missile intersection testing.
In these intervening years, the sabot rounds have incorporated GPS and are accurate to within 3 meters in space at 100 miles of range.
Using a “shotgun” burst shell, and firing 18 shots per minute using all guns, which are independently targetable, you can hit many missiles for a micro fraction of the cost of 1 missile to missile firing.
Cheaper. Faster. Longer ranged. This is a 21st century Battleship.