Edit. If you accept the number of 16 holodecks and that at any given moment there are ~670 people in their free time, you can satisfy the holo-needs of only 2.4 % of aforementioned people.
I'm surprised that aren't lines outside of holodecks...
Actually I'd say that number is wrong. The crew is stated as being 1014, including civilians. So if they run a 3 shift rotation, that means that on average, 676 crew members/civilians are either on duty/working, or sleeping.
that leaves 338 crew members off duty and awake at any given time. So with 16 holodecks, there is 128 hours of holodeck time available for recreation during every off shift. It's likely that one holodeck visit = 1 hour.
That means 37% of those people are able to use the holodeck on a daily basis. Now you'd factor in that people probably don't use the holodeck every day, as well as the option for the other recreational activities available.
And then some people(couples, friends) might use the holodeck simultaneously to run programs together.
So lets say theres 896 of hours available per off shift every week(128x7). And lets say of those 338 crew, they typically use the holodeck 3 times a week. That's 1014 hours needed. So in any given week, only 118 people can visit the holodeck twice rather than 3 times. That's meeting the needs of 88% of the crew on a weekly basis given the 3 visit parameters.
Then you could factor in that maybe 20%ish of those people(68) are using the holodeck with a group of 2 or more. for this argument we'll just say a pair. So the crew needs 912 hours for 3 visits a week per shift, with 896 hours available. Now we're up to 98% needs met.
Not to mention some people would only want to use it once a week, or once a month that will put us over 100%. You'll get the odd case like Barclay. It's no different than people who are addicted to mmorpg's now. But typically, I think people can entertain themselves. And if you're working on a starship, I'd wager most are a bit more mentally stable than a manic depressive with dependency issues. So I'd say 16 holodecks is a pretty realistic number. It's not surprising to me if the holodeck would be unused at a given time.