True. But are we talking about how a given table was playing, or how the game was presented? Because the game, as presented, had you gain, by and large, one or even two levels by the end of the module. You were supposed to be 3rd level or even 4th by the end of Keep on the Borderlands so you could move on to Isle of Dread.
Serial modules like the Slave Lords or GDQ also presumed about one level per adventure.
This is where talking about Old School really breaks down. People presume that just because they played a certain way, that's the way the game was meant to be played. High lethality, glacially slow advancement, all these things might have been true at your table. They were not actually part of the game as presented though. 1st to 5th level? You're basically finished Keep on the Borderlands and a small ways into Isle of Dread by that point. Even the 1e DMG talks about hitting name level in one year of play.
It's so frustrating to try to have conversations about this because you see it all the time. Look at the back and forth I had about magic items.
True, but, that's kind of the point. As soon as we're talking about a DM redoing and expanding the tables, that's just proof that the tables are weighted to produce certain results. The DM wouldn't be redoing the tables otherwise. IOW, the game strongly pushes players to make certain choices. Sure, you can use a polearm, but, you're basically gimping your character doing so. So, everyone takes a longsword because they know that the DM won't put magic items geared to my choices in the game, so, I'll just play the odds.
And, oh look, playing the odds pays off every time.