The creation of the MACH, OTCH, and CT came AFTER the breed split between show and field.
There will be no triple champion, as you define it, until there is first a realistic hope again for dual champions.
I have said it before, and I will say it again, we must all acknowledge what we all know is already true -- the breed is split. Then move the show-bred Labs (read "English Labs" as Wolters and others have documented as their origin during the late-'50s and early-'60s) to the NonSporting Group with that other retriever breed rarely used for sport, the Poodle. Give the spot in the Sporting Group to athletic working Labs, and dual and triple champions will be a real possibility again.
Will the show-bred Labs be excluded from field events? Like the Poodle, of course not. If they can do the work, they should be included. But let's be realistic, just like the Poodle, the show-bred Lab no longer belongs in the Sporting Group. Their only argument is tradition. But that argument doesn't hold water with the existence of the field-bred Lab which rightly does belong in the Sporting Group.
Acknowledge what we already know is true -- the breed is split. And then the Dual Champion and Triple Champion Labrador can be a reality once again.