The collection, transportation, and keeping of native fish is governed by the states. So, a lot will depend on their management objectives and practices. In some states, it requires extensive documentation and permits, in others, it's a matter of obeying the creel limits and fishing regulations.
One other problem with keeping many native is that they often will require a chiller to thrive, and the game fish typically will outgrow the common tank sizes.
For fast growth...Hmmm....For critters, my vote goes to apple snails. Not sure on fish. My raibows got big quick, but then leveled out a bit smaller than full adult size...