Sorry all but why do you say "put a fish on the reel"? Is that a slang saying for catching fish using the reel and the handle or can you use the line to drag the fish in by hand? Does it make a difference or is this "fly lingo"?
Thanks.

Fly fishing definitely has its own lingo. Mend, haul, tippet, euro nymphing...

Say you are sight casting redfish. Using a bait caster, you throw out your paddle tail at your target, reel a little, and the redfish strikes it. The fish is already on the reel from the very beginning. It stays that way the whole fight.

Same scenario but this time with a fly set up. First, you have to pull the right amount of line off the reel. Say the target is 40 feet away. You pull 45-50 feet of line off the reel and pile it in a basket, on the deck, in the water, or at your feet. You pull a little more line off than you might need to hit the target just for a safety margin. Better to have a little too much off the reel than too little.

You make your cast. Instead of immediately reeling, you strip in the line with your off rod hand. No reel involved. The line is sort of pinned between your rod hand fingers. Strip with off hand. Line is in a pile in a stripping basket, in the water, on the deck, or at your feet. There could be quite a bit of it depending on how much you initially pulled off the reel for the cast and how much you have stripped in at this point.

The fish eats the fly. I point my rod tip in the direction I'm stripping from and ideally have been since finishing the cast. You strip set the fly with your off hand pulling hard and fast. Hook is set. Now, it's up to the fish to make the next move. Sometimes, redfish seemed a little confused about just what happened. They won't react violently but kind of sit there working their jaw. Other times, they take off in a run immediately. But that run could be towards you. You are stripping in line as fast as you can. The pile of line off the reel grows. If you had made a long cast and the fish ran towards you in the beginning, the pile of line off the reel is substantial.

But whatever the size of the pile, there is that dangerous time when the fish makes its inevitable charge away from you. It can be sudden and with the line held in your hands it's difficult to respond as quickly as the fish does. The bigger the fish and the lower the break strength of the tippet, the more the danger.

Most of the time in my experience bigger slot reds and slightly over sized fish will make a long run that will quickly eat into the pile of line off the reel until it's all gone and the fish is on the reel. Then it's just a matter of having your drag on the reel right. I start off with a very light drag and adjust accordingly.

It would be silly to me to try to keep the fish off the reel once the pile off the reel is gone. That would require you to either bear down on the fish and put tons of pressure on it to keep it off the reel almost certainly breaking your tippet or somehow in the fight strip more line off the reel.

My old Abel reels are built for this but I've never caught a fish big enough to justify palming the reel. Mostly native trout back in the fly fishing days.

-SECOND THAT BIG TiME!
And if you are wade fishing, watch that fish run right at you and through that floating line laying all around you. By going to the reel whenever possible, it enforces a good habit and becomes a natural reflex over time. It'll then pay off when you have the big one on. At least that's what I preach in my lessons.