Others have noted it, leveling doesn't necessarily make your character better. They just face tougher monsters and the fights take longer. I won't cover that already well-tread ground.
I want to take on the assumption that without leveling, without significant character bonuses earned over time, that a game is only good for a one-shot. Unfortunately, leveling is the default for "character growth" in RPGs because it is simpler than developing a character narratively. Characters growing in a narrative way are much more complex as there are no handy yardsticks to measure it.
To those who think leveling is necessary to hold a player's interest over long games, let me ask you a few questions.
A) Did you ever watch Scooby Doo when you were a kid?
B) Did you keep coming back to see the next week's episode? (okay maybe just the older folks need to answer this).
C) From the first episode to the last episode, how many levels did Shaggy gain? Did he improve in any way or change at all? Nope.
Most sitcoms, cartoons, and weekly TV shows featured no character growth beyond "who's hooking up with who". Yet fans came back for more. They wanted to see the problem of the week unfold, hear the funny quips, and try to guess how it all ends.
Without the goal of levels, perhaps the players will become more invested in the tale. Less "what will my character become" and more "what will my character do". If you can accept and enjoy that playstyle, you don't need leveling to enjoy a game for a long, long time.
