か as a suffix to mean "a few": Why is 何__かがVERB not allowed

Question

Here is yet another puzzling sentence for me from a dictionary I am using:

何ページ か 欠けている。 A few pages are missing. (研究社)

My understanding is that while 何ページ ambiguously means "what/which/how many page/pages," adding か as a suffix to it limits the meaning to "a few pages." This applies to common usages such as いくつか, 何人か, etc.

What I do not understand is why there is not a subject marker after this か. When I saw the sentence, I expected to see が between the verb and the subject. On HiNative, a native speaker gave me either "35ページが欠ける" or "何ページか欠ける," but not "何ページかが欠ける." On top of that, a Google search using a similarly structured phrase "何個か欠ける" yielded 1,700 results, whereas "何個かが欠ける" did none. I messed around using other combinations such as かけている, 欠ける, etc. Still, かが+欠ける is simply non-existent.

Notwithstanding the above situation, usages like "何人かが" or "何個かが" seems to be extremely common (bar false positives), not to mention taking は into consideration. "何人かは" and the like are prevalent as well.
EDITED: This claim was wrong. 何__かが practically yields no results. Please see my edit note at the bottom.

What sorcery is this? Now, 欠ける is plain and simple an intransitive verb, so transitivity being the culprit is out of the question. Other sample sentences in the dictionary show 欠ける used with が/は, and with either an animate subject or one that is inanimate. Thus, these are not the factors either.

My only feasible, makeshift theory is that this is a chance encounter where the denizens of the Net simply do not fancy putting 何__かが beside 欠ける. Not plausible enough as I have nothing concrete to back this up. I am at my wit's end.

<(_ _)>この通りです。よろしくお願いいたします！

Edit explanation:

Sorry about this folks, but I made a serious mistake by assuming Google's search results count was trustworthy. As it turned out, as Eversome kindly pointed out below, "何__かが" actually yielded almost zero results no matter what counter we put in between. My bad.

This change of situation means that my question above was in effect partially based on false assumptions. No, __かが is not allowed at all.

The new question: Why is 何__かがVERBnot allowed?

Answer 1

This is simply because we don't usually use が to express the number of something. I think you already know (子供が)3人いる, (リンゴが)5個ある, (本を)3冊買う and so on are grammatical. Number + counter can work as a noun too (e.g., 3人が集まった), but it's relatively uncommon. In addition, ページ is a tricky counter that means both "n pages" and "n-th page", depending on the context. If you use が, people usually take it as "n-th page".

• 5ページ欠けている。 = Five pages are missing.
• 5ページが欠けている。 = Page 5 is missing.

Likewise, 何ページか欠けている does not require が because it's about the number of pages.

EDIT: 何ページ often means "which page", whereas 何人/何個 does not mean "which person/one".

• 何ページ欠けているのですか？ = How many pages are missing?
• 何ページが欠けているのですか？ = Which page is missing?
• 何ページ読んだ？ = How many pages did you read?
• 何ページを読んだ? = Which page did you read?
• 何人欠けているのですか？ = 何人が欠けているのですか？ = How many people are missing/absent? (The former is more common)

So you have to pay special attention when you use が/を with ページ. 何ページかが欠けている is probably grammatical and unambiguous, but it sounds a little unnatural to me, and it's not something people usually say.