Leveling is one of the most fun parts of FF1. You actually need to invest time and effort in making your party good. It makes it more worthwhile to finish the game rather than breezing through it.
It also adds an element of strategy that is missing from many games. Where do you fight? What do you spend your money on first? Do you save up to get a Silver Sword or do you spend it all on a cheap Short Sword and hope that it helps you level faster in the meantime? How much money should you devote to Pure potions and Heal potions? Is it worth spending money on Tents or can you struggle back to town and use the Inn each time? Is it worth buying Steel armor from Melmond when you're going to get Ice or Fire armor in a little while anyways? Should you buy FIR3 or go back and fill up your 3rd and 4th level magic slots instead?
It also gets you to really experience the game to its fullest. There are few enemies in FF1 that I haven't fought, and that's because you're forced to fight so much for everything. Other games I often find myself fighting certain enemy types maybe once or twice per game, if at all; I never get to see their enemy skills, I never really get to know the enemies at all.