This feature or lack thereof is common enough across language families. Besides Hungarian, Turkish and Georgian, it also occurs in Armenian, Persian and apparently Hindi, which are of course Indo-European.
But questions about popularity are very subjective as it requires us to decide what is a language and how to weight each language, for example Luxembourgish or some dialect of Bengali with far more speakers. Moreover the way the feature works varies a bit, so the classification is not perfectly binary.
The feature is not necessarily about number in the languages mentioned above, but any modifier that implies a plural, including much, many, some or a few. And often redundant pluralisation is theoretically allowed, but just very emphatic or otherwise marked.
In the case of Finnish and Estonian there are some nuances, in theory the form after a number is a singular form, but by the strict test they do not have the feature, the form used after 2 or many is different than that used after 1.
In some cases there is simply a specific word which does not require the plural, for example Italian qualche. English nil, zero and no also have some nuances. In other cases there are certain scenarios which do not require the plural, so for example in English one says fourteen stone, in German eine Million Euro, one orders zwo Bier and drei Stück Flammkuchen, viermal if necessary. In Slavic languages 21, 31... 101... 121... and so on agree like 1. But we would not consider this to be a feature of Italian, English, German or Slavic in general.
More happily, this set of features is relatively practical to test for with machine translation. Even if not completely reliable for each language, it can answer the question about the aggregate.
If Google Translate is to be believed, it is not really correlated with agglutination or other features like lack of gender, as it occurs in Hindi but not in Tamil. The feature seems if anything areal and unstable, that is, it varies between closely related languages.