I approve of this thread on the basis it implies downtube shifters...Not so ambidextrous here. Most everything is done with the right hand when on and off the bike. Keeps the controlling left hand on the more powerful front brake, and with the right gives better feel for fine tuning shifters, less likely to drop whatever I'm handling, grab hold of posts during stoplights, clear debris from tires, control computer/gadget, feed oneself or take a feed in a race situation, make gestures kind and retaliatory, zip/unzip, just about everything with the right hand. Left toe strap with left hand though of course.
Even though I am very much right-handed in most things, my left hand is fully capable of squeezing tightly. I've not been persuaded by those who advocate for front brake on the right because it's the dominant hand. Is your left hand so feeble or your brakes so week that they require that typically slight advantage of handedness? Even though I am far more comfortable using my right hand, braking with the left doesn't feel like I'm sacrificing much, if anything.