Download counts dont need you to embed a unique token.

At the most basic level, you can get this by doing a count over http logs.

To tell how many downloads result in an actual install http logs are not enough. You will get extra noise on top of the data you care about.

Download to install conversion also doesn't need an embedded token.

It could be obtained through other data that doesn't need to track the individual install.

I forget if Firefox has a 'welcome' page that it shows on first launch, but it could serve as the count of number of installs.

I believe Firefox also has an auto update system, so that too could serve as an Active Users count.

Lots of ways that you can derive this data without needing to track individual download to installation.

Even if you do 'install' and 'first run' tracking without the unique identifier you need to have consent for EU citizens before sending the tracking request to Mozilla. As the IP is transmitted you would already be sending what the regulations call 'personal data'.

The ID is just additional data that would probably be classified as PD (personal data) as well.

So even basic install tracking is a no go. I also just don't understand why this would be necessary. This wasn't the case for software for how many decades? It didn't necessarily transmit such information. If it was commercial you probably had something like license server stuff in the later days (before just a number that was checked for validation).

It probably became a thing when the mobile phone with app model rose. There the vendors (mostly Apple/Google) knew the downloads from the app stores and marketing wanted more. Especially when the pushed advertisements for apps.

So companies like Adjust rose to fame for tracking ad clicks to installs, first run and usage stats.

This probably led to others thinking it to be a great idea for general software as well.