Phonemes and Allophones
In English, we have two different /p/ sounds. When you say pin, you use an aspirated [pʰ] sound, and when you say spin you use an unaspirated [p˭] sound.
This may come as a surprise! English speakers generally think of them as being the exact same sound. That's because English doesn't have any pair of words which are distinguished with [pʰ] and [p˭]. When we're small children learning the sounds of English, we don't have any reason to train our ears to hear the difference, so we never learn to tell them apart.
To a Thai speaker, however, the situation is very different! Their language demands that they be able to tell the difference, and so to Thai ears, /pʰ/ and /p˭/ are obviously different sounds. They learn to tell them apart as small children, so to them words like ปา /p˭ā/ and พา /pʰā/ are as different as night and day. They can hear a difference English speakers cannot.
Here are a couple terms we can use to talk about this kind of language difference:
The set of phonemes in a language is the set of sounds a native speaker needs to recognize to tell apart different words. Every language has a different set of phonemes.
Phonemes can be pronounced different ways in different contexts. Each individual pronunciation of a phoneme is called an allophone, and these too vary from language to language.
So in Thai, /pʰ/ and /p˭/ are two different phonemes. But in English, there is only phoneme /p/ with two different allophones [pʰ] and [p˭]—two different ways of pronouncing /p/ in different contexts.
The "F" sound in Japanese
English distinguishes /f/ and /h/ sounds. We can tell apart hat and fat, for example. For this reason, we say that English has both /f/ and /h/ as phonemes.
Japanese, however, doesn't have a true [f] sound. What it does have is a voiceless bilabial fricative, represented in IPA with the symbol 〈ɸ〉, a sound Wikipedia describes this way:
For English-speakers, it is easiest to think of the sound as an f-sound made only with the lips, instead of the upper teeth and lower lip.
And because English speakers are used to telling the difference between /f/ and /h/, a lot of us think of this [ɸ] as being a separate /f/ phoneme. Unfortunately, that's not how most native speakers think of it!
The problem is that Japanese doesn't distinguish any two words like hat and fat, so Japanese ears aren't trained to listen for the difference. And what difference is audible is small, and subject to variation; sometimes the [ɸ] sound is blended with an [h] sound, and sometimes [h] is used where [ɸ] is expected. (See An acoustic study of the Japanese voiceless bilabial fricative for details.)
Instead, what we find is that we have a single phoneme /h/, which can be pronounced three different ways in different phonetic contexts:
は /ha/ [ha]
ひ /hi/ [çi]
ふ /hu/ [ɸɯ] ← The "F" sound is an allophone!
へ /he/ [he]
ほ /ho/ [ho]
In column one, we have kana; in column two, a phonemic representation (notice that all five use the same phoneme /h/); and in column three, a phonetic representation showing the allophonic differences between the /h/ sounds in different contexts.
Since Japanese speakers aren't trained to listen to the difference, all three allophones [h], [ç], and [ɸ] sound very similar. When most native speakers hear ふ, they hear the same /h/ sound as in は or ひ. And loanwords like フープ from English hoop naturally fall into the same bucket. Since there's no /f/ phoneme and no contrast between [hɯ] and [ɸɯ], there's no reason for Japanese speakers to transcribe the former with 〈ホゥ〉. And if they did write the difference, few speakers would observe it in pronunciation.
It's true that English is influencing Japanese, and that these phonemic categories may be changing over time, or may change in the future. For example, younger speakers may be acquiring a ティ sound that didn't exist a hundred years ago, a contrast that exists only in loanwords.
But in many cases there's still no contrast. Even with your example of V, where the ヴ kana is in fairly widespread use, few speakers have a phonemic /v/, a contrast between [v] and [b] sounds. Instead, we find that バイオリン and ヴァイオリン are both very common spellings, and there's no real contrast to be observed.
In short, there's no need to distinguish フ from ホゥ in writing because the distinction isn't relevant to speaking Japanese.