The fact that presidents get filtered out is a god send tbh in case of Iran.
Imagine ending up wit people like Masoumeh Alinejad-Ghomi, Reza Pahlavi, Supreme Grandma Maryam Rejavi (_Masoud Rajavi decided to become against the IR since his or his party was filtered out_) or any other weirdo.
Not so great process, but I don't think letting everyone run for presidency has much of its goodies packed with it anyway.
In either case, Iran's constitution keeps the president above so many levels that having impeachment becomes even harder. Whoever president Iran ends up with, it becomes almost impossible to replace or take them down by Majles.
I don't know, probably a role of Prime Minister will be more suited with some changes to law that person can be nailed down in wrongdoing or pressure to step down, but who knows, maybe that backfires too.
yuck, so complicated :p
edit: some typos