I'm with Richard here. I totally get where you're coming from, but it just doesn't work for a singles title, because those aren't about teamwork or group representation. When you have a tag team, either member can get pinned/submit and lose the titles for the team or the stable. With a singles title, a wrestler is representing himself and uses the title as a backbone to his argument that he is superior to the other members of the roster as a whole; further, the company typically gives people titles as a means of getting them over, whether individually or as a stable member. If in a stable of "equals", a member holding a singles title translates to "this is how dominant our group is, consisting of such members", and serves to get the stable over as a whole.
Regardless of any other reasons, though, if the Corre held tag team gold, say it was won by Slater and Gabriel, swapping Barrett or Jackson for one of them makes sense in terms of one-upmanship. The team is suddenly more intimidating to opponents having to contend with a bigger, stronger guy in the match. Do you think for a second that if Barrett won the WHC and said Slater was going to defend it for him, especially against guys who are bigger and/or further up the card, anyone would be saying, "Wow, smart move"? The Freebird Rule works for unpredictability under less important circumstances.
Getting over as a tag team and winning tag titles can be done by pretty much anyone, whether now or in the past when the titles meant more. Singles titles, especially world titles, mean a lot more in terms of people's careers and lives, how much money they make and how long they can survive in the industry. Applying the Freebird Rule to a singles title cheapens the significance of the accomplishment for the wrestler who won it, damages the prestige of the accomplishment for everyone in the future and cheapens the significance of the lineage associated with it. This is the very reason why having Kelly Kelly involved in the WHC match decision is sold effectively because it's a matter of Edge being completely fucked by a heel GM intent on having him lose the title at any cost, even under ridiculous circumstances, even if Edge was also still involved in the match, hoping to fight his own fight. It was acknowledged by everyone involved, down to Michael Cole, that it was bullshit and Edge was all but certain to lose, which would be a slap in the face to the entire industry. The title didn't change hands for this reason, and Kelly got the pin herself for dramatic purposes only, not because they want this to be a regular thing.
If WWE starts making substitutions a regular, accepted thing and legitimate means of title defense, we risk setting a precedent and having a world title match turn into a comedy segment with Hornswoggle. I don't think anyone wants that, nor do we want a situation where anyone can be substituted into the match for the sake of prolonging someone else's reign. If that was the case, David Arquette would still be champion.