Falls apart right here: "Imagine David. David is an airline captain lincenced to fly B737, B747-400, B-747-800 and any B777" There may be pilots who have flown 737, 747, and 777 before, but there are none (or practically none) who are current in all three at once. To get your currency back in a particular airframe could be as simple as a single check ride with a qualified (and current) pilot if it's only been a few weeks since you've flown last, all the way up to a review test and multiple check rides if they haven't flown in that airframe in quite a while.

And how did David get qualified in each of said airframes? An airline wanted David to fly a different route that used a different plane so they PAID for him to get the training and get certified. That would not happen in a freelance system.

There would likely be a freelance community around each type of plane, especially the smaller commuter varieties, but each pilot would basically be restricted to a single airframe until he/she could afford to pay for certification in a bigger and more lucrative jet on their own.

Would the FAA allow such a system to arise? Probably not. The status quo of having airlines schedule crews on routes that they are familiar with (with the occasional change) seems safer than having every single flight be with a crew that is unfamiliar with their route.