@Phil Glantz is exactly right when he says the appeal to urban (or urban aspiring) younger buyers.They definitely have a more modern look than the Shaker family of face frame boxes that are in every tract/multi-family property that goes up.I used them on several projects in DC and haven't had any callbacks on quality.

Being in LA I'm luckly that there is a big market for Modern architecture and high end interiors.

How modern is the electrical?

Going with white is a safe bet.Many moons ago I had this conversation with one of my mentorsMe "I'm doing a re-mod on a kitchen and am thinking of doing something more modern"Mentor "You remember those kitchens from the 1960's with the olive green appliances"Me "Yeah"Mentor "You don't see too many of those around now do you".

I am looking for opinions, please, on whether a buyer would look for the more modern styles of doors/trim, or whether, because these are in great condition, painting them would be an acceptable option.

It is far better to add real estate to an overall portfolio to reduce your overall covariance.Read up on Modern Portfolio Theory.  

Is their a simple way to modernize them?

We have been through a few renovations of older buildings (1937 would not even be considered middle aged around here) with {live edged} planked sheathing - some balloon framed, some more similar to modern construction.In your situation, I would take the entire wall section back to the studs and outside sheathing and use a closed cell spray foam insulation {if budget allowed, I might take the entire side of the house or entire house back to the studs}.

And the wiring in an old building like that wouldn't have been designed to handle anything like a modern electrical demand so the temptation to do something like that is very strong (because you're blowing fuses all the time).

Makes for a nice modern look and is a pretty durable finish.