I tend to hit left as well and for me it was (is) not using equal support with both hands. When I use the support hand properly I shoot POA. JMHO.
Being able to consistently hit POA when using a 2-handed grip is great. Usually considered more stable than a 1-handed grip.
However, if you start hitting left of POA when shooting 1-handed, that may mean that you've been compensating for a trigger control/press problem by relying upon your support hand.
Might be a good idea to have whatever trigger control/press problem that
may exist be identified and corrected, because there may come a time when the only grip you might be able to use is your 1-handed grip.
I've worked with a number of guys who lean toward the competition type "60/40" 2-handed grip technique, and don't ever
plan to have to shoot 1-handed where accuracy may be critical (think "precision shot", or "head shot") for more than points in a competition.
Once they were required to make consistently accurate hits shooting strong-hand/1-handed, it sometimes fell apart for them. (Now imagine weak-hand/1-handed

)
Granted, shooting from the most stable 2-handed position is encouraged, whenever possible ... but relying upon the support hand to compensate for a strong-hand (or dominant hand, for those of you who don't have a "weak hand") technique problem may not ultimately be an ideal goal.
Like other less-than-ideal habits which have become ingrained, though, it can take some time (and lots of trigger time with corrected technique) to adopt a new technique to the point that it's performed properly & unconsciously.