Is it technically possible to write an open source firmware for the existing wireless chips?

Technically, yes. The big hangup is that spec sheets for these chips are often hidden behind NDAs, so devs are left reverse engineering existing firmwares. This extra barrier to entry hobbles further development for many phones.

Not really, modem firmware even for wifi and BT is pretty much tied down "thanks" to regulations, you won't get far without an exploit bypassing the signature verification. Governments are apparently very afraid of people modifying their chipsets to be more powerful in range than allowed.

Could you link me some of those regulations or a article on it. I am curious

https://www.ecfr.gov/current/title-47/chapter-I/subchapter-A... basically, they use the firmware to enforce compliance with the regs on different regions. If you can load your own firmware, you could make the device no longer compliant.