I actually agree with Woodrack this time, which almost never happens. I would be open to trying a point buy system, but I wouldn't prefer it.
I think a point buy system will encourage people to be as powerful as possible without going over the total. People would think that a character using all the points is where an acceptable character should be. Obviously we don't see many weak or low power characters now, but a point buy system is only going to lower the power level characters can be at, not encourage people to make characters without as much of a focus in powers.
Another thing: When I make a character, I try to give it a power that directly supports the direction I want to take the character in. If it's a Knight Radiant, it means the character is shaped by those Ideals and will probably be progressing through the oaths. When I give a character 2,000 Breaths, its because that provides the power needed for my character to go insane. Admittedly some of my older characters don't do this, but its what I try to do.
In my opinion, requiring a direct plot reason to have each power is an alternative. Just having power so your character won't be outmatched in duels isn't enough. That implies that the most important thing your character will be doing is dueling, and that it will fight in a head on battle usually rather than using cleverness to win. The character actively trying to be as powerful as possible/get as much investiture as possible is also not enough. You could instead start your character at a very low power and RP the character searching for each investiture.
Also, smaller issue, but in a point buy system, there are going to be a lot of eventualities that it can't account for. Talents and Epic Powers both can result in powers that are difficult to count. Weaknesses will need to be figured out almost every time. Skills will also often be unexpected. This is something that could be worked around, but it is still an issue.
On mobile, so I may have deleted a paragraph without noticing. Let me know if something I said doesn't make sense.