Technically, if it's a land line port and still connected to an exchange that hasn't gone completely VoIP (that's a thing where I am), it might actually be possible to build a charger module that plugs into that port.
Would it be worth it, though? ... No.
Low power is supplied over old land-lines for the purposes of making telephones ring and powering other handset bits and pieces, within reason of course. Using it for anything else is undoubtedly illegal as phone lines aren't rated for huge power draws.
(If you're interested, there are videos online where people have hooked up LED lamps etc.)
But, let's say that module existed and was legal. Your niece still wouldn't be happy with it.
To avoid burning out to the telephone line, any such device would have to be a r e a l l y s l o w trickle charge.
I wouldn't even think about it for emergency power outages. A battery backup is a better option.
RS232 is functionally immortal. Its market share in the niches it fills has never -- and I'd argue will never -- go away, or even shrink all that much. It's like those lobsters that don't age at all but if we splice the genes that do that into humans it gives us cancer.
I hate it but as you said it has its niche and there really aren't better options for what it does. If someone else has a means to wire up +100 sensors to one system that doesn't involve enough wiring to encircle an entire city or an unbelievable reliable means to do M2M between two machines that's secure simply because everyone who knows how to tap it has a high paying job I am all ears.
Could work in theory. Back then there it had sonething like 40 volts going through the line and you needed some decent power to make the bell in the phone ring.
But I don't know if that's still in use these days.