Of course those around them are allowed to say "please don't do it" -- but the person who's making the decision might still choose to do it. This is true, independently of whether assisted suicide is on the table. Regardless, getting to have an open conversation about it will be a better starting point for healing, for everyone involved. You can't say "please don't do it" to a suicide note, or ask it further questions so that you can better understand why they made that decision.
You have a profound misunderstanding of how most assisted suicide laws around the world work. Doctors are not demanded to do anything, and certainly are not held to any obligation to end the life of anyone who asks them to. They evaluate whether the request has validity based on medical criteria, and deny it or accept it on that basis. Doctors who object for religious or moral reasons are usually exempt from participating in it altogether. They definitely don't have to do it for people who aren't terminally ill -- although in some legislations, they might be allowed to.
I'm also unsure what you believe terminal sedation and cessation of treatment are. Death is definitely the expected result. Or rather, death is the means to achieve the desired goal, which is ending the patient's suffering -- just like with assisted suicide.
You speak of statistics where people have abandoned their wish to die and lived long lives. Did they live good lives? Can you, personally, promise to everyone in the world seeking assisted suicide, that if they do not follow through, they will live good lives? That their continued suffering will eventually end, or that it will be worth enduring?
I think it's the least you can do, given that you've talked to a dentist once or whatever, and that apparently gives you the moral high ground to make that decision, on behalf of all doctors and of all people who seek assisted suicide alike.