Constitution is already fairly rewarding to invest in for all types of characters, as it provides hit points and save bonuses.
Strength, on the other hand, has historically been easy for many types of characters to intentionally dump as low as possible in order to squeeze a little more benefit out of some other score while suffering next to nothing as a result of doing so.
Also, since the question being answered by the bulk rules is how much can be carried, not how long it can be carried for, strength is the better fit from that perspective too.
