Do IMEI Changers/Spoofers Actually Work?

Before replying to this, please spare me the lecture on the legality of spoofing an IMEI. I get it; it's illegal.

I have read a lot of conflicting information online regarding IMEIs. Some say that IMEI spoofing/changing apps do nothing. Others say that cell towers can still see the hardware IMEI but local apps see the spoofed one. And some say that spoofing your IMEI will actually fool cell towers. I would like an answer to this.

The way I see it, there is no way an app can change the hardware IMEI on the actual modem in a phone. If someone has access to your physical phone, they can open up the modem, and with enough effort, they can find the factory IMEI.

However, if I use a so-called IMEI spoofer like Xposed Installer + IMEI Changer Pro, would cell towers will see a spoofed IMEI? Even this is a bit questionable. Why wouldn't the modem insert the IMEI into the request payload in its hardware circuit? How could an app change what the modem sends out in this case?

If anyone with the relevant expertise could provide an actual explanation, I'd be happy to hear. Thank you.