The use of "depths" in the plural can imply varying measurements or also different acts of measurement with the same result.
At the time, America was in the depths of the Depression.
Here, "in" suggests a region containing many points. It refers to a stretch of time when the Depression was bad but could include variation in the actual "depth." The plural is definitely preferred here.
At the time, America was at the depth of the Depression.
Here, "at" suggests one point in time, when the the Depression was at its worst. The singular is strongly preferred here.
Alvin can dive to a depth of 20,000 feet.
The Concorde could fly to a height of 20,000 feet.
Electric scooters can go a distance of 10 miles.
These three sentences are neutral in tone and typical of language emphasizing accuracy and talking about the maximum capabilities of the vehicles.
Alvin can dive through ocean depths.
The Concord could fly over mountain heights.
Electric scooters can go far distances.
These sentences are fine grammatically and semantically. The first two, in using depths and heights as count nouns, have slightly evocative, almost poetic language, not as appropriate for scientific language. Using "depths" and "heights" in the plural is something specific to these particular words, but suggests multiple occasions, different locations, or different measurements.
Alvin can dive to ocean depths of 20,000 feet.
The Concorde could fly to mountain heights of 20,000 feet.
Electric scooters can go far distances of 10 miles.
These three sentences combine the structures of the first two sets. They are grammatically and semantically fine; however, there is a minor clash in tone, especially for the first two. It is hard to stress evocativeness and accuracy at the same time. There is also a clash for all three in suggesting a precise and vague measurement for the same dimension in the same sentence. If you deleted, "ocean" "mountain," and "far," they would read better as an attempt to refer to multiple trips of any length with one maximum measurement for any given trip.