What a great question!
In general for Hindi speakers it seems voiceless fricatives tend to sound closer to aspirated stops, and voiced fricatives like unaspirated stops.
So फ़ maps to फ and ख़ to ख
And ज़ (and ॹ / झ़) maps to ज and ग़ to ग.
As for why - my guess is it has to do with how these consonants are pronounced. To my understanding “Voiced Aspirates” and “Voiceless Aspirates” are created differently. The mechanism behind भ and ध is different than, say, फ and थ.
(Disclaimer - the below is me paraphrasing a linguistics class I took years ago. If anyone knows more and can correct me please do).
When you make a stop like [p], your mouth closes to build up pressure before it releases it to say the syllable. At the same time, your vocal chords stop so you can build up this pressure and say the sound. You then release the pressure and we hear [p].
So when you say पा your vocal chords stop, you build up the pressure for [p], then you release the pressure. Then, your vocal chords begin vibrating as you say [a].
However, if you vocal chords never stop, and vibrate through this entire process, you’ll say बा.
Now if your vocal chords are too late, and there’s a gap between when you release [p] and when they start you’ll actually say फा.
The “aspiration” is due to a gap between the release of the stop and the voicing of the vowel. (This is called Voice Onset Time)
The phenomenon that produces “voiced aspirates” is different. For a syllable like भा, you’re actually pronouncing a ब, and then when you say the vowel you’re adjusting your vocal folds to let more air then usual escape, so the vowel is produced kind of like a ह (this is called “breathy voice” or “murmured voice”)
This is why in some transcriptions (usually for linguists not used to Indo-Aryan languages) you’ll see फा as [pʰa] but भा as something like [b̤a̤].
My point being - voiced and voiceless aspirated stops are pronounced differently. My guess is this difference is a possibility why Hindi speakers map fricatives differently.
But that’s just a guess.
EDIT: This is also a reason why voiceless aspirates are much more common than voiced aspirates globally. Voiceless aspirates often emerge naturally from VOT changes, whereas voiced aspirates are much less common and almost entirely found in South Asia.
