Do you propose offsetting left or right? How does a track offset fix anything but opposite direction issues. You may trust your gear to be .1NM or .9NM off track; how does it compare with the bloke coming the other way, how good is his gear? Your offset may match the error in the aircraft coming the other way, thus your offset is worth less than being on track?
The "Überlingen" crash involved effectively a 90 degree cross, unfortunately the worst thing possible happened, but offsetting would have resolved naught.
In a perfect world we'd have no opposite direction tracks; but what exactly are they? 5 miles apart, 10, 15, 20, 30, 50, we've got variations of all those. The route structure over the 'Bight' is supposed to assist segregation and separation, but often does nothing in terms of 'separation'; throw in one grey puffy thing that you want to fly around.
Let's not mention 'user preferred routes', 'flex tracks', 'free flight' or 'direct tracking' in terms of this stuff.
Your self initiated offset may assist with opp direction traffic (on your route only), but put you in it with any type of crossing traffic or other method of nav going the other way. So even if everything was "perfect" (all gear very accurate) and everyone was flying .7NM (say) Left, only the truly opp direction stuff is sorted with offsets.
ATC separation standards are supposed to provide 1NM (basic) separation (longitudinal, time, lateral etc.) or the relevant vertical standard; Tolerances are wide and varied depending on ground based equipment and the quality and serviceability of the airborne gear.
I think it is far too simplistic to say an offset = increased life expectancy as you're not the only player in the equation. That said it probably would go unnoticed and wouldn't hurt, even if it won't fix all.