Chahbahar port is barely 72km away and Pak-Iran border is around 40-50 km away from Gwadar, which is starting point of CPEC. Turkey can be connected through Iran, as was proposed in ECO.
As we speak, regional strategic posturing is taking place, just the way it did after Nepoleonic Wars, after WWI and after WWII. The recent defence logistics pact signed between India and US, will now give strategic access to US into the heart of South Asia, thus making sure India's long term strategic interests are aligned with those of the US. This will further tighten the embrace between China and Russia and the role of both vis a vis Pakistan will rapidly increase. CPEC, North-South Lahore-Karachi gas pipeline ($2Billion worth being constructed by Russia), Gazprom's interests in investing in energy sector and recent offers of defence military equipment including the talks going on for SU-35 shows that gradually new strategic alignments are taking place. One can't forget the recent rapprochement between Russia and Turkey and see that development in light of the regional alliances taking shape. It would be natural for Iran to join this group, rather than to tow the line of US and India, which has no regional countries with them other than Japan which is pretty far away.