That's the crux of it, alright.
I just find that randomizing something as central to the character concept as their weapons is too random - you lose the ability to make informed choices, and then it's just gambling, not challenging.
It depends on where the play is.
One characteristic that is common among lovers of 3e is being involved in the game away from the table.
5e is very much designed to be engaged at the table only which turns those players off.
Designing a custom item might be a 'challenge' away from the table but that has no value to me.
I don't see it as gambling at all. But then I also don't see the point of the game to "win" as it isn't a strategy game.
I want things in the game to occur where I ask myself how my character would react and change due to that interaction.
A magic item is a perfect catalyst for that change.
Making it just another part of character creation robs that chance. I don't want to plan what magic item I'm going to have at 8th level (or whatever) when I make my character. I want the character to have the chance to evolve in unexpected directions and then respond based on their existing personality and characteristics.
I don't care about the +1, I don't care about how that impacts the "challenge." I care about what it means to the character to have it.
Keep in mind that 5e is specifically designed without magic items being part of the balance. A character doesn't need to have an epic item specifically tailored to them. Getting one should be a cause of celebration, not just predetermined expectation. That's boring.