So you create your own database (relatives, son's school, etc.)?
It's basically bot blocking for phones the way I block bots. You whitelist your contacts and everything else rolls straight to voice mail. The only way to use a phone, email or website in this modern society under constant bot attack.
Back in the 90s at the peak of telemarketing hell we used an auto-attendant answering machine and screening service provided by PacBell for an extra $20/mo and it was worth it at the time as the calls were relentless.
Real people could get right through, the automated machines got bounced as they couldn't push a button to get past the auto-attendant.
There are machines you can buy for $100 or less that do the same thing that replace your answering machine.
If the power is out, would you even be able to use dialup?
Yes, until your laptop runs out of batteries or in some cases the phone line battery dies. Depending on where you live (rural areas, trailer parks, etc.) you may actually have a battery outside your house provided by the phone company which can only sustain a connection for a limited number of hours before needing to be recharged. I knew a guy that ran a BBS back in the 80s and it would just mysteriously go offline after being up about 10 hours solid and it turned out the battery for his phone line was running down LOL.
Just remember when the original phone network was installed some people actually got phone service before they had municipal power, another clue that phones supply their own power. The only time phone lines have a decent amount of power is in the winter when they crank up the juice to warm the lines enough that the ice melts off so they don't break.
FWIW, I'm not sure if a cable modem would work during a power outage as I have a UPS for my computer and could power it, but I'd need to power the router too, so instead I go wireless broadband (requires less power for 3G) in power outages and never tried the cable but I don't think it would work as I don't think they supply their own power like the phone company does. Another reason NOT to use a Cable company phone. Another reason is when the cable goes down, you can't call the cable company LOL. During a natural disaster situation everyone using cable phones are going to be screwed unless both the power and cable network are online.
Always consider your 911 options when buying a phone, it could be the most important decision you'll ever make for you and your family. For that reason I always have a landline, even if it's just a no frills emergency line, for the simple fact that it has the best chance of actually working in more instances than any other phone service.
TIP: Something most people don't consider during a power outage is the car is a rolling charging station with your power adapters for the phone, laptop, etc. just waiting to plug in! So if the batteries are getting low and you really need to get online after an extended power outage, head to the car!
P.S. I used to work in telephony for Rolm/Siemens and a couple of companies that provided services to the telecom market for about 8 years so I know just a little bit about how these things work. :)