I have a suspicion that you can use all nouns after 'type of' as if they are uncountable nouns regardless of what dictionaries say, e.g. 'a type of pie' instead of 'a type of pies' (if you think 'a type of pie' sounds worse than 'a kind of pie', don't nitpick, it's not the point). Does it mean that, for example, I can say 'a type of missile' instead of 'a type of missiles'? Can the latter be used at all (not just with this specific noun but generally)?
The question relates to phrases of the structure kind of thing, and asks about accepted forms based on the plural forms of the words within the phrase. As observed, any uncountable noun may not appear in a plural form.
In every case, the original form of the phrase kind of thing is the accepted and expected form for the singular number.
Following are the three possible forms of the phrase that include plural forms of some of the words:
- kind of things
- kinds of thing
- kinds of things
All three forms appear in modern English, as a plural form of kind of thing, and none is unacceptable.
Which, then, to choose, when needing a plural form in speech or writing?
Form (1), though found in respectable works, including those of Shakespeare, appears to have extremely limited use in contemporary speech and writing.
Form (2) is in active use, but appears less commonly than Form (3), which receives the greatest support from contemporary grammar texts and usage guides, and seems preferred by many native speakers.
A safe choice is (3), but (2) deserves better than to be dismissed.
(Compared to type, which appears in the original question, kind is a more common word in phrases of the general structure, and will be the preferred example in this discussion.)
Preference for kinds of thing over kinds of things may be more likely in cases of the following:
- An individual is British, rather than American.
- The context is a formal style of writing, compared to regular speech or plain writing.
- The word taking the place of thing is either of the following:
- A noun that has common uncountable usages, even if it also has countable usages.
- A noun that describes a topic in an abstract or technical subject.
Webster's Dictionary of English Usage gives an extended and complex discussion relating to the question (see entry for kind), which suggests that kinds of things may be the wisest and safest choice for contemporary writers, while also explaining that all of the other plural forms have been in widespread use as recently as the twentieth century. The Chicago Manual of Style (16th edition) apparently makes no direct mention of the question, but contains over one hundred instances of the general phrase in the form kinds of things, and none in any other plural form.
Contemporary usage, codified by respected style and usage guides, clearly prefers kinds of things.
A Comprehensive Grammar of the English Language (Quirk et al), despite its rigorous treatment of grammar overall, makes only summary mention of the question (see section 5.6, Partitions in respect of quality), suggesting that kinds of things is a preferred pluralization of kind of thing.
Yet, the question appears to be poorly understood grammatically, and lack of agreement over any correct usage from grammatical rules suggests the occurrence of multiple grammatical interpretations.
In particular, ambiguity may arise, within a natural interpretation of the phrases, over the following two competing grammatical parsings:
- [ kind of ] thing
- kind [ of thing ]
In case (1), the preceding phrase (in brackets) functions as an adjective that modifies thing, the noun. Then, pluralization of the phrase requires that thing appear in plural form, with no clear requirement for kind. In case (2), the phrase following kind (in brackets) operates on it as a postmodifier, the same as the phrase of blue would do in sea of blue. Then, pluralization of the phrase applies necessarily to kind, but not so to thing.
Considering case (2), applying a plural form to thing may be inappropriate. In sea of blue, blue is an adjective, just as in blue sea. Similarly, because accepted grammar allows tree types, but clearly rejects trees types, the interpretation of the phrase of thing as a postmodifier suggests that tree, moved to the of phrase, follow the same pattern as blue, and retain necessarily the singular form.
Further ambiguity, however, arises because English usage allows either the singular or plural form for a word representing a category.
Consider the following openings of two Wikipedia articles, from the English versions:
Elephants are mammals of the family Elephantidae and the largest existing land animals.
The African elephant is a genus comprising two living elephant species...
If, in kind of thing, the word thing may be considered to represent a category, then a singular or plural form seems agreeable.
One advantage of kinds of thing is that it more closely follows the form required for uncountable nouns. Since kinds of rice is a plural form, and since kinds of rices is not on offer, kinds of potato might be preferred, as the world is filled both with much rice and many potatoes, but the measure of neither is relevant to the counting of their kinds.
The form kind of thing is the singular form of the phrase, whereas kind of things is considered plural, but is no longer common.
The form kinds of thing is an accepted plural form, and may be a suitable one, in many cases, but kinds of things enjoys greater support in contemporary usage and better favor from individuals currently. The latter is a safer choice, but some writers may prefer the former for a particular literary or formal style, or because of certain grammatical considerations.
A simple, easy-to-read answer
These types of chairs are not commonly seen in this city.
This is a type of chair not commonly seen in this city. [category of chair] OR
This type of chair is not commonly seen in this city. [category of chair]
All those are standard ways of expressing this in English.
In the third and fourth sentences, a type of chair has no s because it functions like a category.
There is nothing inherently BrE or AmE here at all.
As for one type [of noun], that cannot be grammatical if followed by a plural noun.
One type of [signals a category], therefore, one type of chair.
And: Two types of chair, where chair is a category and therefore, non-countable.
One type of [plural noun: chairs] is not grammatical in English.
PLEASE NOTE: any noun can be used as a category. When it is, it is not used in the plural.
One type of can only be followed by a category-type noun, which means it can be followed by any noun, uncountable or countable, but when countable, it must be in the singular.