I've beaten the first two games many times now, sometimes with a hand-to-hand character. Unarmed is better than Melee Weapons because there is no knockback with the stronger Unarmed weapons. I found that hand-to-hand builds aren't as effective as long-range builds in certain battles. The Military Base, Cathedral, Navarro, and the Oil Rig, as well as certain other random encounters, are much harder with a hand-to-hand character than a ranged character, due to the lack of range of the weapons.

It's not until I get the Super Sledge or even the Louisville Slugger that I actually start inflicting decent damage. But by the end of the game, I'm using the Power Fist in the first game or the Mega Power Fist in the second game. A high sneak skill helps with hand-to-hand characters because I need to get close to my enemies to hit them. Especially against turrets.

As a melee-only character, it's much harder to get into the Sierra Army Depot, even with Sneak. Even the strongest short-range weapons don't deal as much damage as the strongest Energy Weapons and Big Guns against certain enemies, including Super Mutants, Deathclaws, or even Frank Horrigan. Often, as a melee-only character, you need to choose your battles wisely because some are just too difficult.

So I'm starting to wonder if there's even a point to making a melee-only character in the first two games. The second game has a much higher level cap and ranged characters only raise Unarmed for certain quests. Even the very start of the game encourages you to use melee weapons because all you have is a spear. The third game practically encourages you to combine melee and ranged in one character. Hand-to-hand combat, from what I've seen on Youtube, is very powerful and effective in New Vegas. And from what I've been told, hand-to-hand is especially useless in Tactics in the later missions.

With all this in mind, is melee only in the early games even practical or viable?

It's obviously better in F2 than in F1 with the higher level cap and the new perks.

As you said, knockback wastes precious AP chasing enemies instead of attacking them. This combined with the low AP cost of unarmed attacks makes them better than melee weapons. It's basically what makes Dogmeat so deadly in F1, except you can actually wear armor to stay alive.

You need all the AP you can get, including Bonus Move to reach enemies quickly. Then you mostly start punching them in the head/eyes repeatedly, which has a high chance of knockout, blindness, and even instant death regardless of damage dealt. Having so many attacks per round makes fishing for crits easier.

You can also cripple an arm to prevent them from using most weapons, or cripple a leg so they can't escape. Frank Horrigan himself is nearly helpless with a broken arm or two.

Sneak skill is kind of odd in older Fallouts, but it can be put to good use, particularly if you manually enter combat mode before using it.

I find that having good Unarmed skill is actually the easiest way to get started in F2, whatever you may end up doing afterward.

Melee is better in FO1 because:

1. Bonus HtH attacks is available already at level 6 as opposed to 15 in FO2
2. Supersledge is available very early on (the moment you enter Hub), whereas supersledge in FO2 is a very endgame weapon (around San Francisco, if you don't skip cities, or New Reno, but you have to become a Made Man prematurely)
3. Fast Shot AP reduction in FO1 applies to melee weapons too, you can have 10 attacks per round with the supersledge.

Knockback is not a problem, never go after enemies. Instead break line of sight behind a doorway and let them come to you. If you knock them back, they'll have to expend AP to get to you. And they shouldn't be able to shoot at you if you break LOS. The only maps where you can't really break LOS easily are desert random encounter maps. The answer is to not fight there.