Eventually the fish will reach it's maximum size.
I'm not sure what you're saying here. Of course a fish will grow to ITS own max size. But if you're saying the fish will definitely reach the max
recorded size of that species, that's wrong. Most, even given optimum care and feeding, will not reach record size.
I do understand what you're trying to say though, I think. They should easily reach or exceed average size in a properly maintained aquarium.
But I do disagree with Moontanman that you can expect a Channel cat to only grow to 18-24 inches given the right care and condition. Channel cats, like many other catfish, will quickly grow to a certain size and then their growth will slow significantly. Given a long time, and proper care you can definitely expect most channel cats to exceed 18 inches. I've known a ton of people with catfish ponds (not aquarists ponds, but actual fishing type ponds), and the fish were put in very small, fed normally and reached over 18 inches. I would say 18 inches is relatively small for a channel catfish. Caught in the wild (not force grown) I've caught MANY a channel cat that was over that size because they had the conditions to reach larger sizes, and conditions in the wild aren't usually as optimum as we can create in an aquarium setting (perfect water quality, constant food, etc.).
COMMON size on fishbase is even listed as 22 inches, max being listed as 51 inches.
I do somewhat disagree with overfeeding (catfish will eat until they nearly explode, so waiting until they're full is overfeeding), but even feeding moderately it will just take them longer to max out if you give them good water parameters and quality food. Making sure not to overfeed does not ensure a smaller mature fish, it simply slows the growth rate and makes for a leaner fish, which will hopefully curtail health problems normally related to overfeeding.
Regarding channel cats being active fish - compared to what? They are fairly inactive during the day, laying on the bottom and barely moving. They can be pretty active at night when hunting, but they don't necessarily feel the need if they are well fed. Viewing channel cats in a very large aquarium, you will probably notice they often hover in one spot, even given sufficient room to swim. I still wouldn't personally want to keep them in a tank they can't comfortable swim around in though, and such a tank would have to be fairly large.
Aquiring an aquarium that will house them to their commonly attained size (22-24 inches, and a 125g is too small for a fish of that size to live comfortably, IMO, even given good water quality) and planning to upgrade or transfer to a pond if they grow further would be optimum.