I would think that a 19 year old furnace in someplace like Louisiania,
where presumably it doesn't get used all that much, would be OK.

Please keep in mind the furnace is also being used as the air handler
for the AC. I'm thinking the AC may be used a fair amount in a place
like Louisiana. Any chance a newer furnace could reduce the electric
bill?

I didn't think of that. Probably because I think of the blower motor
as a separate piece, even though it's not. I wouldn't worry about the
blower motor breaking. Blower motors are realtively cheap and easy to
replace yourself. I've done it once.