Counties with a large college population vs counties with large college populations

This is really splitting hairs, but I can only see this difference:

in counties with a large college population

-in counties which share one property in common (that of having a large college population)

In counties with large college populations

-corresponds to the explanation you have already given ("the plural form of population corresponds to the plural "counties"), so the emphasis falls more on each county having this property, rather than on what makes them a group.

I don't know about every day usage, but in written texts, Google Books gives preference to counties with large populations, which I did not expect, but there you go.

Short Answer

The short answer is that population and populations are two distinct ideas, and there is a difference if one talks about the two. Population, which is treated as a mass noun in the singular, and populations is treated as a countable noun when referring to a collection of distinct groups of people. Which is primarily determined by the context of the passage.

Long Answer

Before we tackle your question, let's take a detour to review. Let's examine two similar sentences.

S1. The sailor sailed over the water.
S2. The sailor sailed over the waters.

This highlights the difference between countable and mass nouns. A countable noun is one that normally is experienced as a collection of objects. For instance, let's consider water. In day to day experience, one generally experience water as the fluid known as liquid. Pure water is essentially a collection of H2O molecules which are imperceptible directly, so water is conceived as a mass. One can have more or less water when one has a mass of water. Sailors, on the other hand, are not imperceptibly divided and reconstituted as groups. Thus one more formally speaks of having more or fewer sailors. In less formal usage, this difference in grammar is frequently blurred or not observed at all.

Now, in the examples above, what seems more natural is the first. Waters doesn't sound right if one uses frequency of occurrence as a measure. In fact, in normal speech, one almost never hears waters used in the plural; however, technically speaking, once can count waters, if one considers water to refer not to the substance, but to the body as a whole. Here in the Chicagoland, we drink (fluid) water from our tap which comes from Lake Michigan. But if we would like to go sailing, we could sail readily on one of five waters (as in bodies of) called the Great Lakes and remembered by HOMES: Huron, Ontario, Michigan, Erie, and Superior. Thus a sailor can sail on the water of Lake Michigan or the waters of the Great Lakes (which collectively is a lot of water, indeed!)

Now, in your example there are two meanings at play between your two sentences. Let's simplify:

S1. I travel to counties with a large college population.
S2. I travel to counties with large college populations.

If S1 sounds more "natural", I'd guess it's because it is used more frequently in speech, however, there is nothing agrammatical about S2, and looks like it might enjoy an advantage among the more literate. Think about the use of 'who' and 'whom' or the subjunctive 'was' or 'were'. Strictly speaking, they mean different things. In the philosophy of language, one might discuss ontological commitment. For the beginner, this simply means that:

S1 claims there is more than one county each of which has one college population.
S2 claims there is more than one county each of which has more than one college population.

I suspect most counties in the US have at most one nearby college, and therefore one college population. But in a metropolitan area like Cook County, there are many colleges and universities and therefore it is fitting to say that the county has college populations (Loyola, UIC, University of Chicago, Northwestern, etc.).

Now, in regards to your Google search, you searched WITHOUT the noun-as-adjective 'college', so that again changes the meaning. This time, we are concerned about non-qualified population within a county. The qualification is one way of expressing what linguistics calls hyponymy. A college population is a type of population. Since population is broader than college population, it usually implies that there are other hyponyms. A county population has many types of populations. Asians in a county, mathematicians in a county, and college students in a county are examples. Thus without the adjective modifying county, it's much easier to see why one might refer to a county with large populations. Demographic analysis by nature is interested in what can be called 'sub-populations of the population of a region', but it's easier to just call them 'populations of a region'. Fewer syllables, fewer letters, and less typing.

The use of plural or singular is related to the subject of the sentence not the subject of the article as a whole.

Since the end of August, deaths from the corona-virus have doubled in counties with a large college population, compared with a 58 percent increase in the rest of the nation.

Answer, This relates to Counties with a large number of college students (the number of colleges being irrelevant to the fact). Hence population is used as opposed too populations.

(2)

In counties with large college populations and where deaths had increased notably in the fall, local health officials offered a wide range of explanations.

Answer, This relates to local not regional Health officials, so the number of offered explanation relates to local populations Not the regional (county) population. Hence populations is used as opposed too population.