Is そこはかとない really a single word?


(I understand that "word" is not an especially rigorously defined concept, but
I hope the question is still coherent.)

In the computer game series [空気]{くうき}[読]{よ}み, I noticed that the player's
efforts may be rated as 「そこはかとなく読めてるっぽい」(localized: "very vaguely
considerate").

Jisho [gives a base
form](https://jisho.org/search/%E3%81%9D%E3%81%93%E3%81%AF%E3%81%8B%E3%81%A8%E3%81%AA%E3%81%84)
そこはかとない:

> I-adjective (keiyoushi): 1. faint; slight; vague; nebulous; indeterminate;
> tinge of ...; touch of ...​

I can't find any evidence of kanji being used to express this, even very rare
ones. It doesn't make sense to me to have this many kanji-less kana in a row
for a "single word". To contrast: I know that e.g. よろしくおねがいします is commonly
written all in hiragana, but it also seems fine to write as よろしくお願いします; and
[宜]{よろ}[敷]{し} and [御]{お} and [為]{し} at least exist - such that 宜敷く御願い為ます seems
at least theoretically possible, if extremely chuuni. But _for そこはかとない I can't
find anything analogous_ 1.

When I first saw this, I assumed the は was particle-wa, which naturally
suggests a decomposition そこ + は (topic marker) + か (interrogative particle) +
と (quotative) + ない. However, I can't make any sense of that grammar (in
particular the は-か combination), and certainly can't relate it to the
dictionary meaning.

Is it a set phrase consisting of multiple lexical items? Or is it some kind of
lexicalized expression? In these cases, how can we parse it? Is some kind of
elision involved?

Or is this just a word that has always just been a word, that somehow never
involved any kanji, and suspiciously looks like it has all these other short
words and particles in it?

1 Unless, of course, it does break down into pieces the way I imagine, in
which case I guess [其処]{そこ} and [無]{な} would apply. Anyway, the point I am
trying to make is that the existence of those kanji helps establish よろしく and お
(prefix) and ねがい and します as separate lexical items.

