Yes, I was just quoting OP (as a non-native speaker of English I also prefer "I doubt that" or "I have doubts" (except when in singular).

This said, some may copy from their language 1:1 - in French you say "j'ai un doute" (I have a doubt) so this may also be the reason. There are also other versions ("j'en doute" - I doubt that, or "j'ai des doutes" - I have doubts)

Singular "doubt" is pretty common, but almost exclusively used when indicating a lack of doubt.