That was my fear your answer would be, in short
iOS doesn't support other devices telling it to send a text message.
Yup, that was my guess too. One of the main reasons I dumped iOS. Their stuff is so proprietary, it just doesn't play well with anything.
Went to Galaxy Note8 after being a long time curser of the early days of Android. Took a leap and never looked back. Android has come a long long long way since I last used. No more lag, stuff makes sense, and it integrates with freakin everything. Literally integrates to my Windows10 laptop and I send and receive texts on it all day long. I barely pick up my phone when I'm using my laptop.
That said, back to the car -- Bluetooth works perfect, and I can reply to texts, but note the reply function isn't a custom type function - it uses predetermined texts that you set up. So they can be like, "ok" or "hey, driving, text you soon." or anything else you want them to say, it gives you like 10 slots to customize. But after every text, it says "Sent from my Mazda fast text system" or something like that. So that's a little dumb, but at least people know I'm driving and to leave me alone.
I know it's disappointing to know your iPhone doesn't work with it, I was in the same boat when I bought mine. But I was ready for an upgrade and that helped me make my decision -- hopefully this sheds some light on your issue