Its a good idea. Everyone in the household who can legally do so should get their permit, and ALL handguns should be listed on ALL the permits.
Back in the late 1960s, my parents were in four car collision. They survived (although a couple people did not). It was after that that we realized that if something had happened to Dad, all his pistols would have to be turned in. He owned 6 handguns, which was more than anyone else we knew in our town (the next highest number was 2).
At that time, if we turned them in to the State police, they would be held a certain amount of time (90 days, IIRC) and then, destroyed. If we turned them in to the local Sherriff, and applied for a permit, they would be held until the permit was approved (or denied).
At that time each gun was listed on the permit by maker, caliber, barrel length, and serial number. Mom applied, and get her permit. Both my brother and I applied (and got) our permits when we turned 18. (at that time, the age of the permit holder was at the issuing judge's discretion, as was everything else about the permit) Also, at that time, permits were good for life, unless revoked. And not valid at all in NYC. And there was no concealed permit. Your pistol permit was required for ownership, and valid for open carry (other than in NYC) only.
Are the permits today still the unlaminated paper they were then?
I went into the Army in 1975, and left New York state. After my service, I wound up living on the other side of the country, in a place with a much friendlier attitude towards handgun owners.
In 2000, New York contacted me, and since I was "no longer a NYS resident", the informed me my permit was no longer valid. And, they wanted it back! They wanted me to send them the little paper card with my picture & thumbprint on it. The one they issued me back in 1975! AND, they wanted me to tell them what happened to the handguns that were listed on it!
(the guns on my NY permit were my Dad's (and Mom's). I owned no handguns of my own at the time I got the permit)
Needless to say, they did not receive what they considered a satisfactory response....
in 2003, my Dad passed away (Mom had gone earlier), and I returned to NYS to help my brother deal with things. Some of Dads guns were going home with me (rifles), but the handguns we had to have shipped, FFL dealer to dealer. We (my brother, since he had the permit) had to drive 80 miles to find a dealer to ship them. (When I lived there, I could ride my bicycle to 4 different shops within 20 miles...)
As to everyone who comments about "silly laws" and "you should move", the laws under which we grow up and seldom silly, we are taught to think of them as what is right, and proper. After all, its the law! it isn't until you live somewhere else, with different laws that you really get to understand the difference. I was happy, and even proud to comply with the NY law when I lived there. It wasn't until I lived elsewhere that I realized just how complex, costly, and onerous NY law really was. And I think its worse today.
If your family, social, and economic situation allows, move. If it doesn't, obey the law and do what you can to get it changed (*and good luck with that*). New York State is a great place, but it is, and has been badly run for generations. And by badly, I mean with respect to gun rights. (its badly run a lot of other ways too, but this isn't the place for that discussion).
Seriously, get everyone who can in the household a permit, and get all the gun on all of them. Its basic CYA for you, and everyone else. And remember, any crime (including traffic violations) could result in loss of the permit. That too is at the whim of a judge.