Pronunciation of 'to have' in different contexts

The verb 'to have' can be used to mean two things in English:

1. 'To have' means exactly the same as French 'avoir', German 'haben', Italian 'avere' etc.

2. Followed by 'to', it means 'must'. 'To have to' - 'devior', 'mussen', 'devere'.

I have noticed that in the first instance, it's pronounced 'normally', in comparison to how it is pronounced in the second.

Here is a phonetic conjugation of the two instances of this verb as I see it:

1. Hav, had, haz
2. Haf, hat, has (soft 's')

So, 'I 'hav' a dog', but 'I 'hat' to do it, she 'has' to go, they will 'haf' to be there'.

Has anybody else noticed this?

It is so in American English, but if I am not mistaken, you are British, aren't you? Is it so in most British dialects too then?
I hav two things to do, I hafta do them.

That's interesting that it happens in American too.
Yes, I'm British - and yep, it happens mostly here too. Nobody really notices it, I just randomly picked up on it.

I have wondered why this happens. Could it be that since the beginning of the word 'to' following the form of 'have' is voiceless while the end of 'have' is voiced, it's easier to just devoice the v?