There are "different" than Club Champion fittings (this is probably for the regular guy).
Club Champion has its place. That being said....
Different example, not putters:
There are qualified Master Fitters at places like Edwin Watts (ex: Houston) that can take the time to fit you either to a brand you want with a specific shaft (irons/woods), or go completely club agnostic putting you in a club/shaft combo that uses the stock shaft options (at no additional cost to you from off shelf and they can be many), or tune a shaft to a club just for you (extra). If you find a head/shaft combo that is "stock" to a brand, it is no more cost than buying off the shelf, typically except for grip specifics. They will order what you need from the manufacturer, you just have to wait a couple weeks. Even with lie and loft adjustments. Why not? at off the shelf prices.
You can definitely use Club Champion. Hear it is a great experience, but you pay for the fitting in a few ways. Upfront for the specs to go buy elsewhere, or you can pay for special shafts in heads and that can turn your clubs from a stock fitting (and special can be done here as well) at Edwin Watts in Houston, or spend a whole lot more buying a custom set from Club Champion.
Obviously, if you are quite accomplished, Club Champion may make a lot of sense, dialing in specifics to a fine tune. For a high, mid, mid-low, or perhaps low handicap player, why by a set off the shelf when someplace like Edwin Watts with Master Fitters on staff can put one into a set of irons/woods/Driver utilizing factory available (and others) shafts at no additional cost over stock that best fit them, rather than buying something off the rack and working themselves into it.
I thought I was a buy off the rack guy based on past history many years ago. Was not a bad player back in the day before a long, long hiatus. Was going to buy off the rack, but took advantage of the "free" fitting sessions at Edwin Watts (Houston) to see if it was worth it. Will probably never buy another iron set or driver without it again. Went club agnostic, and ended up with the best fit of clubs for my game I ever would have thought of.
Sorry, edit to add:
This was not a putter. It was a bag full. No fitting fee. Even asked if a tip was traditional, as I was going to do so after two sessions. He said he would not take one if offered, because of the bag of clubs purchased. A putter fitting may warrant one. Dont know about a putter "fitting".
"Green" is the new RED.