Cool BreezeI am walking. Walking is an adjective?
"allegedly"

See below.
From Introduction to the Grammar of English (Huddleston, Cambridge Textbooks in Linguistics)
... participles are said to be 'verbal adjectives'.
First example given:
He was telling the truth.
Later:
... a present participle ... allegedly has adjectival properties. I say 'allegedly' because it is difficult to see any significant functional resemblance to an adjective ... [in the first example on the list].
He goes on to say that the -ing words in such examples are clearly verbs, while in other contexts they are clearly adjectives.
_____
With respect to the original question then, I suppose the more accurate description is that participles are either parts of verb phrases or are adjectives. In either case, a participle -- being verb or adjective -- cannot be the subject of a sentence unless it is in the cleft sentence structure, as illustrated earlier in the thread by GG. I think that's the only structure that allows a participle or an adjective to be promoted to the status of a noun phrase so it can be a subject.
At least that's my claim. Maybe someone can provide a counterexample. That would be instructive.
Edit:
'Destroyed' is the best description of that town.
Here a participle (adjective) is promoted to a noun and is the subject of the sentence. So there are cases other than the cleft sentence structure that allow it. Nevertheless, note the quotes. It works in the same way that anything in quotes can be promoted to subject:
'Xygneoowytoeyy' is a nonsense word.
'got into the truck' is not a complete sentence.
_____
Your question opens up a good many sticky points in the terminology. Do we (Can we) talk about certain structures by naming them without regard to their function in context? Or not? Probably not. Is love a noun or a verb? Only context will tell.
Cool BreezeTo hear him sing is an unforgettable experience.
to hear him sing is a sentence with a non-finite verb used as a noun phrase in a higher level sentence. The idea is that the terminological identity of a word or group of words may change depending on which level in a hierarchy of clauses it is considered. At the lowest level of the "tree",
to hear is indeed an infinitive (a non-finite verb), but in the context of the whole sentence (higher in the hierarchical tree),
to hear him sing is the subject of the main clause, is nominal in nature, and is called a noun phrase. (Infinitives are often nominal in nature, so this is not surprising; for example,
[I want + noun phrase] can take either of these forms:
I want some pizza. I want to sing.)
Cool BreezeUsing an infinitive as a subject may not be common in American English
Actually, infinitives are used in AmE as subjects. The location geographically or historically has nothing to do with it. But infinitives (and their complement(s), if any), taken together, can make noun phrases.
To be absolutely precise, it is a noun phrase (NP) that must be the subject of a sentence. I oversimplified by saying 'noun or pronoun'.
CJ