I see your issue and sympathize. Constitution is the one stat that no one wants to dump into because of the need for hit points but only get a really good number if that number isn't needed elsewhere.
In my game Con ranges from 12-16 I think. No one would ever consider putting an 8 or even anything under 12 unless they had to. Consider those character types, the standard array, and likely dump stat for instance:
Strong-guy: Str, then Con most likely. Dump is probably Int, Wis, or Cha.
Agile-guy: Dex, then maybe Int or Cha depending on the build, but Con would likely be third best or fourth--certainly not the 8! Dump is likely Wis or Str.
Smart-guy: Int, maybe Dex, Wis, or Cha, but then likely Con as 3rd or 4th, and likely dump the 8 would be in Str.
Wise-guy: Wis, maybe Str or Dex, but if you are fighting at all much likely Con is 2nd, 3rd, or maybe 4th... Dump here is probably Dex, Int, or even Cha.
Charm-guy: Cha, maybe Dex or Int or even Wis, but again Con is likely 3rd or 4th. Dump is likely Str, but others are possible of course depending on the build.
Tough-guy: Con, then probably Str or Dex or Wis, likely dump is Int.
So, yeah, you are unlikely to willingly see a player dump into Con unless they have a compelling story reason or other purpose for it. After all, who wants to have less hit points???
As for what exactly to do about it, I couldn't tell you much right now as I'll have to think about it and maybe discuss it with my group. I never played 4E or even 3 or 3.5 much, so I am not familiar with some of your thoughts linked to those editions.