At what point to put fish on the reel? Simple, when the fish dictates...and not a second before. The fight of the fish should determine the answer to the question.

It really doesn't have as much to do with fish size/weight as it does with the ability of the fish to have its own way with whatever set-up you are using. Fish that are accustomed to using flight to avoid predation are prime candidates for getting them on the reel.

For example, a 1 pound bonefish can quickly overpower just about any unsuspecting angler who thinks they can manage the initial run by hand. It isn't the size but the fight in the fish. The inexperienced angler will quickly learn that to be successful at most salt water fly fishing, it is absolutely imperative to effectively learn to use the reel.

In freshwater situations, in my experience, it isn't anywhere near as likely to need the reel...exceptions being those fish that once lived in salt water e.g. many of the salmon types, steelhead, and even tidal run cut throats and dollies and char etc. that return or otherwise find themselves in freshwater. Stripers often fit into this category. Again, it isn't the weight of the fish so much as the fight of the fish.

There is a reason for the revolution in large arbor reels...and it isn't for holding line in your hand. They are not just for show. Large arbor reels are one of the greatest innovations, IMO, in fly fishing equipment ever.

I put this fish on my reel

I try to put any fish I can in the reel just for the fact that, if I don't, I end up with fly line wrapped around everything in my boat, including the trolling motor, push pole, casting stool, rod rack and my feet. It just saves me a lot of headaches to keep the line on the reel.