Sure, by creating the friction tunnel, you are less likely to get distracted online, which makes self control easier.
But the thing is we are smart and computers are fast; meaning most software-based friction tunnels are quick to undo.
I did something similar to what the OP described by solely using the Mullvad Browser, which is in permanent incognito mode.
The moment this introduced friction in some nuanced way that I had not foreseen, I just switched back to my main browser as I could not think of a way to handle this edge case.
For me at least I think the friction tunnel needs to be inherently physical. Using an old computer (with a new one not in the same room) is a much better friction tunnel than changing your browser.