Yes, you are describing a common situation. The “super sharp” part is good, but the “small” part is not. Many of today’s monitors are of such high resolution that the default text size in the monitor’s “native” resolution is too small for comfortable viewing at a typical viewing distance.
This it what I had in mind in the initial post.
With apology, the following is somewhat long and tedious.
TLDR version: I still think I need a sub-4K resolution monitor smaller than 27", for technical reasons.
Popular opinion seems to be that for a given monitor, if 2560 x 1440 resolution is good, then 4k (3840 x 2160) must be better, right? Not necessarily - it depends on the monitor size, the viewing distance and the user’s visual acuity.
The sharpness of text in a monitor’s “native” resolution will usually be better than that in an electronically-modified resolution, even though the text size (in modified resolution) might be larger. The iMac display might be an exception - see below. I am looking for a 24-25" monitor whose “native” resolution is “perfect”, meaning optimal sharpness at a text size that is comfortable for my viewing distance.
Apparently the monitor manufacturers are responding to demand by offering “4K” (3840 x 2160) monitors. 27" is a popular size, but I need a smaller size for the space available and appearance reasons. I suspect that “4K” 3840 x 2160 resolution for a 24" monitor would result in a default or “native” text size that is too small. For me, at least. My theory is that my optimal resolution for a 24" monitor is greater than 1920 x 1080 but less than 3840 x 2160. 2560 x 1440 is available in at least a few 24" monitors, so could this be the right choice? I’m casting about for others’ opinions or experiences.
More pertinent detail for those still awake 
- the native resolution in the 27" so-called 5K iMac is 5120 x 2880, or 218 ppi (pixels per inch), if I measured my screen correctly. This is a gorgeous screen, but overkill if your viewing distance is like mine (about 32"). If you adjust the iMac’s display resolution to its “smallest” or “More space” setting, the text will be quite small. At this setting you could display many windows on the Mac’s screen. The text would be too small for most, however, at a normal viewing distance. The iMac’s “default” display resolution is, appropriately, two steps up from this. It appears that the “default” resolution is really not the screen’s “native” resolution. Apparently Apple has done some excellent engineering to achieve a very sharp text display at a non-native screen resolution.
Other, cheaper and non-Apple-engineered displays typically do not share this characteristic - that text display at non-native resolution is as sharp as text display at maximum, or native, resolution. This explains my search for a non-4K monitor smaller than needs to be smaller than 27".