Actually it’s not just about what you bring up but about language and the meaning of words. Words change over time.
In the past, back when we had record labels that were huge, the distinction was more clear. You had song writers, arrangers, musicians, artists, recording engineers, mix engineers and mastering engineers. The “producer” would oversee the production process, not fiddle around with synthesizers.
But over time several of those roles began to merge together, and a lot of people who started making their own music started calling themselves producers. They may have been mostly writers, or mostly musicians, but since they didn’t hire a producer it sounded nice so… and it wasn’t completely inaccurate either.
So anyway, I think that’s a roughly accurate description of the past use of that word.
As for your actual process, these days; “who cares?” Just do what is convenient and works for you. The benefits of you leaving things the way you like them is that then it’s the way you like it. Especially if you’re the one mixing it saves you time.
On the other hand the benefit of getting rid of some parameters is really more about starting with a more clean slate. So you sit down, listen to the song/recording for the “first” time, and then decide on a mix approach to bring out the best of the music/song. The more you commit to sounds and automation etc before the “mix session” the less freedom the mix engineer has.
It’s a double-edge sword. I’ve had mix sessions where I went down one path the artist didn’t expect and they loved it. In some other cases the opposite effect. I honestly don’t mix much music at all these days and I don’t miss it to be honest. To me music is close to my heart and once I feel strongly about a music mix it’s super-annoying to have to compromise… if I care about the music that is.
So anyway: If someone sends me music to mix I’ll simply talk to them ahead of time so everyone knows what to expect. If I get to do what I want then maybe I’ll use what’s there already, but maybe I won’t. I don’t think there’s a right or wrong answer to your question - it just ‘varies’.