You were told only part of what happens.
The full system is:
The final –(e)s of this form is pronounced:
/s/ after unvoiced consonants except /s, ʃ, ʧ/: /kIks, pʊts, kɒfs/
/z/ after vowels, diphthongs and voiced consonants except /z, ʒ, ʤ/ : /hʌgz, siːz, leIz/
/Iz/(or/əz/) after /s, z, ʃ, ʒ, ʧ/ and /ʤ/: /bɒksIz, bʌzIz, wɒʃIz ruːʒIz, kśʧIz, ʤʌʤIz/
You wrote: "We can very well say /artʃs/ or /artʃis/, /diʃs/ or /diʃis/ I've just tried saying it , and it went like a breeze"
I'm inclined to think that, without fully realising it, you inserted a short schwa or /I/ into your/artʃs/ and /diʃs/