As a native speaker of Russian, where [k]/[kʲ] and [g]/[gʲ] are phonemically distinct, I've always been intrigued by the fact that several languages that don't have that distinction, and are in fact hardly "into" palatalisation at all, tend to favour what I'd describe as [kʲ] and [gʲ] realisations over "plain" [k] and [g], or at least go for something in between. This includes many varieties of English, as well as French, Swedish, Persian, and perhaps some others that I'm not aware of.
In most if not all of these cases, the plain and palatalised versions co-exist as allophones, depending on position; [kʲ]/[gʲ] is especially frequent word-finally. On the other hand, this doesn't happen to any other consonants: the English take, depending on the speaker, is about equally likely to be pronounced as [teɪk] or as [teɪkʲ] (or close to it), while in no English accent does tape even remotely sound like [teɪpʲ]. Also, the phenomenon appears to be rather sporadic; it exists in French but not in Spanish, in Swedish but not in Danish.
Have there been any studies or proposed explanations as to why and under what conditions these palatalised allophones develop?