You can easily put the gun somewhere safe.
Ah, but if the gun is somewhere safe, you're unlikely to be able to get to it quickly. For a gun to be viable for self defense, you need to be able to get it and load it in a very short period of time. Otherwise, you might as well invest in a squirt gun. If you put the gun somewhere that's actually safe from a child, you're also making it considerably harder for you to get access to the weapon quickly. Those critical seconds could mean the difference between life and death.
In any case, if I was going to use an electronic lock, I would much rather use a RFID lock over a fingerprint lock. There would be a much smaller chance for error.
That seems like a perfectly reasonable alternative. I certainly don't think laws need to mandate a specific technology, just a minimum certification level or some such, which different weapons could achieve in different ways.
Also, if you have children in the house, they should be taught gun safety and that if they even touch any gun without your permission, there will be hell to pay.
I completely agree with you about teaching your kids gun safety, and even though I don't intend to have guns in my house, when I eventually have kids, they will learn how to properly unload a firearm. The problem with having guns in houses with kids comes when they invite other kids over. Chances are, your kids' friends haven't been taught about guns, and they may not know not to touch them, or worse, might think that they're toy guns. That's why particularly in households with kids, having some form of electronic safety is a really, really good idea.