That distinction doesn't make sense. You could just as easily say websites are not always commercials products, whereas browsers often are made by for-profit corporations.
A website is non-commercial when it isn't doing commerce.
A browser doesn't have that simple test. It can be used to do anything.
Therefore, the commercial website made by someone who chose to make it commercial needs to be regulated, as opposed to trying to regulate every browser.
(As an aside, you likely don't know how many browsers exist.)
Websites that collect personal data on their servers are data controllers. They have to ask for consent for this reason. Browsers also need to ask for consent if they collect personal data but that is indepedent from the data websites collect. Being commercial or not is irrelevant. The point is collecting and processing personal data. Furthermore, a browser runs on your machine. Unless they send data to some server, any data processing on the browser is happening on your machine.
That doesn't have anything to do with this conversation.
This conversation is about making it mandatory for browsers to automatically communicate consent so that we're not bombarded with visual requests for consent.
And the counterargument is that it is responsibility of websites to ask for consent because they are the ones collecting and controlling the data, not the browsers. Browsers can send DNT and whatever headers all they want. It is websites that should respect them and abide to them. "Targeting browsers" is pointless.
Well, there's little for websites to respect if we don't ensure popular commercial browsers have the capability to send the necessary headers, and that these headers actually reflect user choices, even if the corporations behind them don't want to.
So it's not pointless at all. It's rather quite an important half of the equation. How is it going to work at all without that?
You seem to be anti-regulation period.