I don't want to argue, since you seem unwilling to budge on the idea, but a few points of clarification:
1) The first bolded part. It's not subjective that it's
likely that the other str-based melee character also pumped his strength score; that's not a statement that the term 'subjective' can be applied to. If you were referring to whether or not the person thinks it's worth it to use of of three attunement slots for a bonus of 1 to attack and damage, well then yes, it's relative to other attunement items being available in the campaign. Compared to other items requiring attunement, however, it's starting to look less subjective, at least mathematically.
2) The second bolded part. Yeah, at that point, it's a nice add-on for str-saves and checks (not a lot of str saves, but whatever). Was the idea for the girdle of giant strength "Boy, it will really help with Athletics?" If so, then it's doing its job well. If you have an idea inspired by Thor, for instance, of putting on his Belt and becoming
even stronger than it doesn't work (though it did both things in 3e).
3) Third bolded part. No offense, but that is flat out untrue. It can't be exactly the same unless it is actually exactly the same. 1e is a one-time choice; 5e is a choice made every 4 levels (or more frequently). Investing in a stock once then just living with its performance is very different than revisiting your portfolio and making decisions every x number of years.
4) Your end statement. I'd be surprised if anyone ever said those words too. Doesn't mean they didn't feel it or think them. Besides, the point being made by Paraxis (I believe) is that this is a false dichotomy; a girdle that enhances strength can be a flat score, but a large bonus accomplishes a greater multitude of things, including still being of benefit for the target that, classically speaking, would get the most use out of it.
I think this is highly subjective, not only because it depends on the scenario, but the attitude of the player with that option. You might not think going from an 18 to a 20 is worth attunement, but I do. Also, not every str based melee PC in any group I've ever played with all had maximum strength. An item like that was always useful to someone. And thirdly, even if you have a DEX based melee fighter, having a major bump in strength? Yes please! It would sure help all those times I have to make a STR save or check.
Not necessarily true. Most methods in AD&D, you didn't just end up with a STR score your rolled. You rolled all six stats, then assigned them. That means you made a choice on what abilities to focus on; which ones to make the investment. That means it's exactly the same as deciding to put your ability bumps in a certain stat insofar as the base argument Paraxis made. I.e., choices on how to build your stats being made moot from an item later on.
And I'm here to say, I don't recall a single situation ever in 35 years where a player felt they were being cheated because they put their highest stat (16) into strength and came across a girdle or gauntlets of ogre power, saying, "If I knew I was getting this, I would have put my 16 into CON instead. I feel cheated."
Not one person.