I don't know how to start. Understanding NAT won't help here.
The MAC is individual and bound to a network device. Lets take a look at the OSI Layer, we're talking about Layer 2 (Ethernet Frame/Data Link). But the tracker will work much higher at 7 (Application).
Sidenote: We're only using NAT; because IPv4 won't provide enough Addresses. It will be solved by using IPv6 ...
What is the advantage of a static MAC?
Think big. In an Enterprise environment, it is good to route packages, based on the MAC. Just take the Laptop from the WLAN in your office and take it to the conference room. The network is knowing your MAC and can provide exact the same permissions, without any manual reconfiguration.
Why should I want a stealth mode?
When I am in a war or hunting, I don't want to be seen. But every day? Many private firewalls offering a 'stealth mode'. This means the system will drop ICMP requests, and don't send an answer. But a lot of applications (Game Server, file transfer services, Printer/Scanner (send to PC)..) are using Ping to check if the system is available. I choose not to be seen and choose not to use comfort.
In case of untracker, I'll see the same double side. the ad-companies can't see me and analyze my behavior. But in the end I don't see less ads, only less relevant.
The MAC is not the only fixed value. There could be also a fixed IP (common in company networks), the hostname is relevant, the opened sites.
Every morning workdays between 8:40 and 10:00h I'll open elive, xkcd, dilbert, questionablecontent, LinkedIn and my github ... My 5 minute routine at the first coffee. Regardless of the MAC, IP, Hostname, everyone who has access to some of the 5 websites is able to track me, no matter how my MAC, GEO IP or Operating System ...
Instead of 'how can I be better than the system', just ask 'do I want to expose this information?'
Today I'll keep track of some wish lists at amazon, I share documents at googledrive and watch movies via netflix. This don't mean I have secrets and some excel files are local and some music is still only on my phone.
Just try to be healthy paranoid. 'They'll' get the data anyways. and when 'they' have to guess, based on location, age and size of your shoes.