Provided that OP has plenty of spare time to go to Mazda dealer several times trying to fix a single problem. Software updates rarely can fix any hardware problems. OP should insists his Mazda dealer to replace the entire infotainment unit at the first place.
LOL you've got to be joking. Might as well ask for a brand new car hahaha
First, if you have an issue with a car that is under warranty, you take it to the dealer. That is common sense. If you aren't willing to take the time to have the dealer troubleshoot the issue, then you fix it yourself (at the risk of voiding your factory warranty) or you live with it. Tesla offers mobile service appointments, but if you don't have a Tesla, you take it to the dealer for professional diagnosis.
Second, what makes you think that it's a hardware problem? OP states that the system crashes and reboots when using Bluetooth. Works fine when using the radio. If it was an issue with the CMU, it would crash and reboot regardless of the audio source. Now, it's possible that it could be a hardware issue with the physical Bluetooth receiver/transmitter, but it would be easier and cheaper for everyone involved to do a firmware/software update or reflash first. The reflash takes minutes, and it won't cost OP anything. Anyone who's ever troubleshooted anything at all knows that you start with the small stuff first. If you're getting engine vibration and poor mileage, you don't bring the car in for a valve cleaning. You check the engine air filter, check the motor mounts, then have the intake valves inspected with a boroscope to confirm if the valves need to be cleaned, and then you bring the car in for a valve cleaning. Everyone follows this process to avoid unnecessary spending, the dealer is no exception.
Third, software fixes can most definitely correct some (but not all) hardware problems, within reason. Consider the OTA OS updates you get on your phone. They wouldn't be doing these updates if they didn't make the product better or fix identified issues.