They'll take us out at night, slowly picking us off.
Correct. While early lynches are usually worthless, they aren't in practice, as I can name some very recent games where scums got picked off early.
The other thing is, we have a finite number of lynches, and a finite number of murders. Because the game is in flux, we don't know the precise number of either. However, lynches would be our only tool to defeat the enemy, and when we choose not to use them, or we cannot use them because of a game mechanic interfering, we lose out on our number of lynches that we can use. As the number gets smaller, the odds of victory by random chance approach zero.
While not lynching will increase the number of murders it takes to bring us down, assuming one mafia family, every murder will be a townie. Whereas, assuming a random lynch candidate, every lynch will not necessarily be a townie. By that reasoning, we need a maximum number of lynches.
If two mafia families, it's technically possible to win by the mafia destroying each other without out help, but it's very unlikely.
Every murder brings us closer to defeat, and every lynch we lose out on brings us closer to defeat. Our only path to victory is the lynch, unless we have vigilantes.