app specific passwords

Why is there no way to recover an app specific password?

I have apps that sync across 4 devices. If anything happens and I have to create a new app specific password, I have to have all 4 devices right there and enter the new password on all 4 devices before logging out of the Apple security site. The alternative is copying down the password, which goes against all the password security suggestions.

Yes, security is important. But with this system, I spend so much time setting a new password, then creating a new password every time I use a device I didn't have handy the last time I created the password, into an endless loop of creating a new password every time I use the app.

OK, I'm off my soapbox now. And off to get my other computer that stays packed in my travel bag so I can once again create another app specific password and enter it into all the devices.