Allowing everyone completely free and unfettered access to photograph anything they want is (despite protestations to the contrary by the uninformed) a significant security issue. It's easier to understand this if you have military experience, especially experience dealing with an enemy that doesn't wear a uniform and has no pretentions of honor or fairness or any notion of leaving innocent civilians out of things. To really understand this, you need to think like a terrorist.
Let's say you want to attack the Statue Of Liberty. The resources you have available to carry out the attack are 1 SUV, a small boat, 10 kilos of c-4, 5 men willing to die for their 72 virgins, 8 AK-47 rifles + 4000 rounds of ammunition, 3 9mm pistols + 2000 rounds of ammunition, 5 Kevlar vests, 2 RPGs, and 10 fragmentation grenades. What kind of attack might you be able to carry out with a reasonable chance of success (success being defined as maximum damage to the statue and maximum civilian casualties)? To answer these questions, you need to do a thorough reconnaissance of your intended target. Getting detailed photographs of the structural supports of the statue is critical to determine whether the explosives would be enough to topple/destroy the statue, but even more important is photos of the access to the structural supports (doors, passageways, etc), the physical security measures (type of door, type of lock), and other protective measures, such as photos of the guards, especially if you can determine what weapons the guards are carrying and duplicate their uniforms from the photos. Knowing the weapons carried by the guards is important--if you know that your vests are capable of stopping bullets from the guards' guns, that means you can plan for much more head-on confrontations with the guards than if you know your vests will not stop their bullets. Knowing the type of doors and locks between you and the target will tell you how much time you will need to breach the doors and reach the target, and whether you will need to allocate some of your explosives to breach the doors instead of blowing the statue itself.
Yes, you could probably find a structural drawing of the Statue online that would be sufficiently detailed to accurately calculate how much of a given explosive you'd need to collapse it, and where you'd need to place the charges for maximum effect. But that drawing isn't going to tell you what security measures are currently in place (where are surveillance cameras? how many guards are there? how alert are they? what is their response time? how secure is their base of operation? what kind of doors/locks are between best access point and target?, etc, etc.), or how long you'll need to fight off the guards while the charges are placed, or the best way to utilize the crowd of visitors as human shields to delay the guards' response. You could use Google Earth to figure out the best route from your base to the statue to launch your attack, but that isn't going to tell you the patrol routes of the Coast Guard assets in the area, or how quickly the guards at the Statue might coordinate with the Coast Guard if they saw a suspicious boat coming in. For the kind of data that an attacker really needs to be successful, there is no substitute for in-person reconnaissance done by someone who knows what kinds of things to look for that might spell the difference between success and failure. Photographs are an important part of such reconnaissance, no question.
That said, there is a shortage of common sense regarding police response to and treatment of photographers. The focus of a common tourist is going to be different than that of a terrorist, both in what is photographed and how. A tourist is going to generally go for the "postcard" type shots, while a terrorist is going to focus more on things like storm drain grates, doors and locks, security camera locations, security personnel and their equipment, etc. A smart terrorist is going to try to behave as much like a tourist as possible, but a trained observer should be able to tell the difference, especially if the photos taken are examined. The kneejerk law enforcement response is to simply ban photography altogether, but a smarter alternative would be to allow photography even in potentially sensitive areas, and observe the photographers. If you see someone a little too fixated on photographing security cameras or door locks or security personnel or other things directly related to planning a successful attack, you have an opportunity to disrupt a potential attack in the planning stages you would have missed if photography was banned altogether. And the majority of tourists can go on about their business without intrusive restrictions on normal tourist behaviors.