If CON becomes slightly less essential, this strikes me as good. With their pitiful skill ranks, a 12 Intelligence could let a Fighter actually gain a skill or two (particularly if you house rule away class/cross class skills), or having a decent Charisma might encourage a PC to opt for some different strategies (intimidate?) on occasion.
No offense, but especially at the lower point-buys you won't see points that would have been in Constitution placed in Int, Wis, or Cha (particularly for Fighters). You'll just see higher strength and dexterity, which will make them do slightly more damage, slightly more accurate in ranged combat, and may increase their AC. In exchange, they will have lower fort saves and about the same average hit points.
Consider a fighter who would normally have put a 14 in Constitution. He still wants a bonus, so he leaves it at 12, which is reasonable under a max hp situation. With the 2 floating points he could raise his dexterity, intelligence, or charisma 2 points or raise his strength 1 point (assuming he began with at least a 14 in strength). Its possible that he takes one of the non-physical stats (particularly if he's interested in multiclassing), but I don't think you'll see it. YMMV
Even more important than averages is the MINIMUM. This is particularly important for high-HD classes.
In my experience, the average is a minimum, if you decide not to take a re-roll, or roll at all. This does not mean that the average is the least I have seen a character get for a level, despite those rules. I have had it explained to me, in fact, that you have a greater chance of beating the average on 2 rolls than you do by taking the average. So, statistically, you will come out ahead in hit points if you always roll twice (Assuming you are forced to take the second roll, not the higher of the 2). However, if you get a lot of low rolls early on, this may force you to dislike the character or get rid of them prematurely.
And I stand by the fact that while it spells DOOM to get a very low roll for a high-HD class, it is quite joyous when they max their roll. The highest I've ever gotten for a barbarian was 11, and I was quite pleased. If I low roll on the first die, I generally take the average rather than re-rolling, especially with characters who need hp. Personally I just disagree with the statisticians, especially when you start at level 1
Finally, it creates a reason to have a high con as a high-HD class - to try and devalue those low rolls. Maybe you only rolled a 3 on your d10, but with your Con bonus you're still getting 6 hit points for the level. If the 10 con rogue maxes his roll, you'll still outstrip his hp (based on first level differences and con differences over time). When the fighter doesn't need a high Con, it just feels less like d&d to me...