No! ... er, well... if you
crush the front brake lever and lock the front tire you'll knife the wheel over to one side or the other and go down on yer shoulder, not "flip over the handlebars" as is the common thought (that's on slippery - the front usually stays in place and the rest of the bike swings around if you've
good traction, but the effect is the same) - but as the front wheel is about 80% of the stopping power on two-wheeled vehicles I'd say it's worth it. During braking your inertia causes your center of mass to shift forward, reducing the weight on the rear wheel to the point of being useless insofar as braking traction is concerned - this is why it's so easy to skid the rear tire.
I've even had people tell me my rear tire was off the ground just a little when I brake really hard, I was screwing around at work the other day lol, checkin' to see just how quick I could stop my bike with my spiffy new "performance" brake pads. While I DO recommend learning what your "panic stop" distance really is at speed - be careful, it's sketchy heh

and remember that while you won't go
over the bars - you might still face a shoulder dig.
I hardly ever use my rear brakes as a result - I only use it to "balance" the braking power if I'm on a slippery surface like wet grass or sand. Mostly I only use the front brake to stop/slow with a finger on the rear brake lever - just in case. It's not just bicycles - this is the same technique I used with all my motorcycles, delivering pizza in the city, racing moto, even just normal putting about.
This is why you'll see that while many motorcycles and even most cars have disks in the front, the rears are still old fashioned drum brakes. While drums are more prone to "fade" from heat - it doesn't matter as much/happen as much in the back.
As for the conflict of levers on the handlebars - while there's the "dual pull/two in one" levers, I really prefer more control over which brake does what. My solution to this was to pull in my brake lever (mounted horizontally) and mount the clutch lever outside it at a roughly 45° angle down. This allows me to "two finger" the brake and pull the clutch simultaneously. I pulled in the other brake lever just so they'd match - I'm a slave to fashion lol
It's actually quite comfortable tho it does take some getting used to;