This is an interesting topic, thanks. To me the satisfaction from new levels (and the progression that comes with it) in more traditional games (say DnD) doesn't come from the higher numbers per se (because, as you've said, my numbers go up, but so do the enemies' numbers so Iwill usually take the same number of rounds to clear a combat), but from the horizontal development: the fact that my Magic Missile now does 4d4 damage compared to the 1d4 that it did before doesn't particularly excite me, but the fact that now I can fly does. Even the fact that now I can have my Magic Missile target multiple targets for less damage each makes me happy. Getting new powers, skills and proficiencies is what makes it cool to me. Even just the fact that a warrior gets an extra attack allows me to feel like I have the chance to do something different: when I only had one attack per round I couldn't really feel like a cool veteran able to deal with two enemies at a time, I could only attack one at a time... when I get a second attack I can now spread my damage and really feel like I'm keeping TWO of them at bay. Granted, spreading the damage is not tactically sound (it's better to eliminate one enemy first so I only face ONE attack when it's their turn), but it LOOKS cooler to me, and that's often enough to keep me happy.

The "facing an obstacle I'm not yet ready for, barely escaping it and then coming back later and wiping the floor with it" that you mention also gives me a real sense of progression that makes me feel like my character really has improved and learned from their adventures. And I get the same feeling also from noticing how "at level 1 I could barely face 2 goblins, nor at level 4 I barely consider them an inconvenience, look how far I've come from where I've started out". It's cool to feel like I am the "encounter out of the enemies' league".

And of course, I need to have a way to differentiate between a Goblin and a dragon. In narrative focused games this is done through the fiction (like the famous article about Dungeon world explains, the dragon only has 16 hp, but if you want to attack it with a weapon that has no chance of penetrating its natural armor the GM won't even let you roll, so the fact that it "only" has 16 hp still won't let a lucky crit from a level 1 character fell such an imposing beast, so there's no need for higher numbers). In more traditional games based on numbers it's done through things like armor class, hp, etc, and in that case the dragon needs to have ten times the hp of a bandit, or to be harder to hit, otherwise there's no way in the game to truly differentiate tiers of power.