But then you have to remember the counter setting for that website. So it's almost the same problem; I could just add a 1 to the end of my master password for that website.
The profile is also used to store other site-specific attributes, like if it has some weird password rule that requires pure alphanumeric or a specific password length.
This blog post[0] shows how LessPass lets you change passwords per site, and get around tricky password requirements.
[0] https://blog.lesspass.com/lesspass-how-it-works-dde742dd18a4