The problem with "Point Buy" systems

Let's look at a few arbitrary systems where two players get 500 points to build their respective sides. 

First, a miniatures game. Player 1 picks a fairly balanced squad with a 100 point leader, four 50 point veteran offsiders, and eight 25 point regular troops...for a total squad of 13 troops. Player 2 picks a legendary 250 point hero, three 50 point veteran offsiders and four 25 point regular troops... For a total of 8 figures. The main differences between the teams are that Player 1 has 4 more troops to play with, while player 2 has a monstrous character on the table who is more than twice as strong as their opponent's leader. In a straight up battle, that 250 point miniature will probably be wiping the floor with everyone else on the table. This isn't even pushing the issue to the extreme of Player 3 who lays a single 500 point miniature (typically reserved for 2000pt army games) on the table.

If, instead of a straight up fight, a multiple objective scoring game is played, then Player 3 with their single figurre doesn't stand much of a chance, both of the other players should have no trouble scoring two or three objectives while leaving the third player to hold a single point with their lone figure. Yet in the multiple objective game, Player 1 has around 50% more actions to play with than Player 2 (due to having 13 figures compared to 8). They'll have an edge in this scenario, until fights break out, and they see that edge whittled away by the 250 point hero. Knowing what type of game you're going to play can allow you to optimise your force, but we don't want everyone playing exactly the same thing because that doesn't make things interesting.

Second, a tabletop game. It's a superhero game. Player 1 chooses a balanced character, spending 100 points each on a pair of powers; one combative, one investigative. Then they spend 75 points each on  their social skills and intuition/common-sense. 50 points each go into contacts in the local police force and the city bureaucrats, and the last 50 is spent on a pair of character quirks that may or may not come into play but are interesting. Player 2 makes a one-trick pony with a single 300 point combative power, then spends 100 points on an endurance ability to weather anything that might be hurled at him, 50 points of contacts in the local criminal underworld, and finally a pair of 25 point character quirks because he doesn't want to be accused of being too one-dimensional.

Again, head to head, Player 2 will walk all over Player 1. But in more rounded play, Player 1's avatar in the world will be more capable of pushing the story forward and will be a better all rounder. 

Where I see the problem is when the little things happen in this second case. During the every day events of the world, Player 2's character really can't do much and they get bored in the game, so the GM tries to balance things out to give them a share of the action. Then combat occurs, and Player 2 sines by obliterating everything. The little things that Player 1 paid attention to are ignored, and only the big things get the GMs attention...since Player 2 has the biggest of the big things, they get the attention more often. It's not a one off, I've seen this happen many times.

Is it a sign of bad GMing in the context of point buy systems? Probably. But I've heard so many people say that there's no such thing as a bad GM, there are just GMs who are suited to styles of play different to what you might like. Personally I think that's a load of crap, there are certainly bad GMs, and if you've seen six groups come out of the same GMs room at a convention, all asking for their money back because they thought the session was a waste of time and money (and two more groups pulling out because they didn't know who was going to be GMing their session, and only just found out, but knew the GMs modus operandi from previous conventions), you'll know exactly what I mean.

Is it a sign that "point buy systems" are inherently bad? That can be a factor as well. How do you define a point buy balance where one thing is more directly powerful in a specific situation, while something else is less powerful but can be used in a diverse range of scenarios? Somewhere in the intersection of character design and scenario design, there can be balancing factors brough into play, or unbalancing forces. No system is ever perfect, but "point buy systems" seem quite capable of abuse. 

At least with a randomised character generation system, you know that things are going to be unfair from the very beginning, without a facade of balance...but that's a whole other rant.