Whenever I look up a transcription for a word containing [o], it's either an [oɪ] diphthong or an [oʊ] diphthong. Is it not possible to pronounce [o] without gliding through [ʊ] too? Is it possible, but English simply doesn't do it? Or, do monophthong [o] words actually exist in English, and I simply haven't been able to find them? EDIT: This question regards any dialect of English.
In Standard American English and Standard British English, no. /o/ is always realized as a diphthong, primarily [oʊ], or [o] may appear in other diphthongs, e.g. [oɪ] although this is usually closer to [ɔɪ]. In some dialects of English, notably Indian English and I believe some types of Caribbean English too, /o/ can be realized as a monophthongal [o].
According to the table in Wiktionary Appendix:English pronunciation words like not are pronounced using ɒ,ɔ or ɒ and words like force are pronounced using ɔː, oː oɹ, ɔɹ similar to words like horse (depending on the dialect of English).
So if you require
o and do not allow
ɔ there is still the possibility of the long
oː or the
o before an
Words like load, go, row are sometimes treated as having the phonological vowel /o/. That is a phonemic analysis of the where vowels are tense or lax, so we have the opposition i/ɪ, e/ɛ, u/ʊ, o/ɔ. Phonetically, it is usually recognized that the mid vowels are diphthongs, written as [ei], [ɛɪ] or [ɛi] among others. I think the phonetic facts support [ɛɪ, ɔʊ] over the competitors. The quality [ɔ] also occurs before [ɹ] as in "core". There are American and British dialects (spoken in the north, in both cases) where "goat" is [go:t]. I can't say that there isn't a dialect where short o in got, rot, sop is phonetic [o], but I haven't heard of one. I would say that short monophthongal [o] is non-existent in English.