In modern grammar, why are gerunds and participles grouped?

From Language Log

...I was happy when Geoffrey Pullum and Rodney Huddleston, in the Cambridge Grammar of the English Language, presented a clear and compelling argument that "A distinction between gerund and present participle can't be sustained" (pp. 80-83 and 1220-1222). They therefore use the merged category "gerund-participle". I hope that most of you will be as happy about this development as I was. The core examples of the present participle are its uses as a modifier or predicative in sentences like those given in CGEL 3 [14]:

The train is now approaching Platform 3.

The train approaching platform 3 is the 11.20 to Bath.

He threw it in the path of an approaching train.

The core examples of the gerund are its uses as the verbal head of a noun-like construction in sentences like those in CGEL 3 [19]:

Destroying the files was a serious mistake.

I regret destroying the files.

CGEL:

Historically the gerund and present participle of traditional grammar have different sources, but in Modern English, the forms are identical. No verb shows any difference in form in the constructions of [14] and [19], not even be. The historical difference is of no relevance to the analysis of the current inflectional system […] This grammar also takes the view that even from the point of view of syntax (as opposed to inflection) the distinction between gerund and present participle is not viable, and we will therefore also not talk of gerund and present participle constructions […]