Maybe, maybe not.
And 3" is not the only option in 12 gauge. My HD shotguns are 12 gauge 870s and they're loaded with 2 3/4" loads. More than adequate.
And do not make your choice using youtube vids. Base it on actual in your hands experience.
I do consider a 410 viable for HD, especially in the hands of elderly or physically limited people, but it's certainly not the One Size Fits All optimum choice.
And, since expertise depends on use, there's so much more that can be done with a 12.
The common mistake made is to buy a weapon, load it up, maybe shoot a few rounds, maybe not, and then stow it while thinking one is prepared for a crisis.
This bothers me even more than PGO shotguns, the job market, or the current mess in the government.
One needs to gain proficiency with one's weapon(s) before one can be ready to protect themselves, their families and communities. That takes a round count.
Skeet with a 410 could work. Hunting rabbits and squirrels with the lilliputian bore is fun, but not enough rounds get fired to move up the learning curve much.
And unless you reload, 410s run a couple dollars a box more than the bigger but more used 12 gauge.
Clay games can certainly up that round count. And if one can smash 2 4" discs moving on different vectors in a short time frame time after time, larger, slower,closer targets present little difficulty.
If circumstances require operating outside the house, like many citizens have done during things like NOLA during Katrina, the 12 has the advantage there.
So, try different things and make your choice based on what works best for you....