Quare ascribo scribitur pro asscribo?
Just speculation, but probably because when (a)d- prefixed to a verb beginning with s+vowel and assimilated to (a)s-, -ss- would be pronounced longer than a single s, but when (a)d- was prefixed to a verb begining with s+consonant and assimilated, -s- would not be lengthened because the entire consonant cluster would be already pronounced longer than a single consonant without lengthening -s-.
This happens with other verbs begining with ad- prefixed to a consonant cluster beginning with s-:
aspergo
asto
aspicio
Non caret ratione quod dicis, quo tibi gratias.