'Old' houses in the US are different than old houses in the UK. Old in the US usually means 1930s/40s/50s and the majority of that housing stock was poorly constructed leading to the problems that @toomuchtodo alluded to. In the few places where we truly have old houses (19th century) - the North East and central parts of some cities - they do, usually, command a premium.
Usually when I've seen 19th century homes for sale at premium prices, it's because they're of a desirable architecture in old-money neighborhoods and have been well maintained for their entire existence. I think it might be a bit of a survivorship bias.
Look at the HVAC system (typically boilers/hydronics of various vintages). If they're in good shape, it's likely the rest of the home as been similarly kept up, as that's one of the more expensive systems in such a home to keep in working order.
