We've been down this path before.
Those little Sunbeam dryers (and or similar from other brands) were indeed for drying Madame's or Mademoiselle's dainty things. Slips, nylons, drawers, etc...
This maybe before some member's time, but not that long ago (and maybe still for some) all "nice" girls hand washed their lingerie, nylons and other undergarments nightly (or soon as they could get round) before going to bed.
If one grew up with females (or married to one, *LOL*) there was the nightly ritual of having to use a loo filled with dripping underthings that had been hung to dry. Hence that famous scene in film "Goodbye Girl" where Richard Dreyfuss rants "And I don't like the panties drying on the rod"....
Part of this was of course was lack of a washing machine, and or one that could do small loads without wasting gallons of water. This and or a machine that was gentle enough not to damage fine undergarments. Nylons in particular were expensive (and hard to get during WWII), so you took good care.
Other part comes down to simple hygiene. Perspiration is acidic. If left on garments not only is the whiff hard to remove, but it can damage and or discolor fabrics. Girls and women were advised to launder their girdles, bras, etc... soon after wearing in order to minimize these issues.
Finally the other reason was simple practicality. People didn't have the vast wardrobes of today (well maybe the wealthy), and that applied to undergarments. So you washed what was worn to have it ready for another day.
As electricity became more common all sorts of appliances popped up to deal with various issues, and these small dryers were one of them.
These dryers were often given to young girls or women as presents for various occasions. Their use must have delighted the males in any household that bathrooms were free from drying underwear.
http://www.retrothing.com/2009/07/wagner-portable-personal-clothes-dryer.html
Then you had contraptions like the Tide Dryer from Ronco.
https://www.ebay.com/itm/RONCO-TIDI...m=263823282000&_trksid=p2047675.c100005.m1851
Basically a bonnet hair dryer that also did smalls.