i recite a good friend of mine: "if you go to a standard gym, it's important how much weight you can lift. but i like the miltary style of crossfit, you just have your goal and you have to achieve it, no matter how long it takes, 5 min, 20 min, 30 min."
There's nothing unique about that. Don't let the hype fool you. You can have your own gym and create a random amount of work for members to hit on a certain day and just tell them to do it in their own time.
Crossfit did not invent this.
At the same time, Burger King didn't invent burgers but because of the genuis marketing, many people probably think they do. And if there's no burger king in your area, you're guaranteed to make money by opening one rather than your own Burger Brand which will need to develop it's own reputation before becoming successful.
If you label it crossfit you'll get a little influx of members who like crossfit and they'll pay whatever you want to charge without question and be loyal to you. You'll also get a whole bunch of people who will say, "i would love to go to that warehouse gym, it has everything i want - bars, free weights, bumper plates, ropes, plyo boxes, etc etc etc, but it's a crossfit gym and I don't like crossfit". I.e me. One has opened right around the corner from my gym. If it wasn't crossfit I would train there.
If it's just picking up speed in your area then you may even get little influxes of MMA types who think it's perfect for their sport, for a while, until they realise they're probably safer doing the bodyweight style circuit training they were doing before because they get hurt less - and an athlete should NOT get hurt in the gym.
Anyway, i'm probably a bad person to ask. I'm sure you could make it work. I hear some CF affiliates put their own stamp on it, work outs are less random, exercise choice is safer, members are sceened before they start, etc. Then it's not really crossfit but if you still have that logo then no one will know the difference, could be best of both worlds.