I would rather not carry a gun that I can't shoot well one handed. I can shoot the G19 I've been carrying for the last 6 months or so, and the pistol that I took my last training course with (CSAT), one handed, off hand (strong hand), with almost the same precision and accuracy as I can two handed at 7 yards. Two handed at that distance my best precision is around 1/2 inch, and this opens up, oh to maybe an inch one handed. Shooting weak hand, off hand, at the same distance, my group can open up to 2 inches however and admittedly I don't practice using my weak hand as much as I should.
Where my shooting noticeably suffers while shooting strong arm one handed is in rapid fire (controlled string with one shot for each sight picture). I haven't checked my splits shooting rapid fire one handed, but I'd say I'm at least twice as slow.
I also admit that I don't practice shooting weak hand one handed rapid fire except for in context of this drill: high ready position strong arm one handed, extend out, two rapid "flash sight picture" shots, transition to weak hand, two rapid shots. So, I definitely need practice shooting weak hand only but that's another story.
Lastly though, doing the wall dry fire drill one handed (strong arm) forced me to adjust my strong hand grip and trigger finger placement because before it wasn't truly neutral and when I shot one handed I'd throw my front sight slightly right. When I shot two hand isosceles this problem wasn't visible because the added stability of the two handed grip hid the problem. Improving my one handed grip though so that I attained a truly neutral grip/trigger pull has not only helped my shooting one handed, but it definitely helped my two handed shooting as well for both speed and accuracy/precision.