The objections to this possibility and the concerns people are expressing about it are really interesting. This is already a reality in some countries and to my knowledge it has had zero impact on the number of suicides nor has their population size decreased because the number of approved cases is still very small. As for having to die in an empty room in some cold hospital, that's not how it works. You can have your loved ones present or the physician&staff can even come to your home so you pass away in your own bed if you like.
Personally I would love to have a system like this in place in my country, especially if they offered counseling for the loved ones of the person who makes the request. Imo it would be so much less traumatic for everyone involved than having to discover your child's/partner's/friend's lifeless body, wondering why they did it, if you could have helped them, feeling guilty and having to make all the necessary arrangement while grieving and in shock. Of course many families will oppose it no matter what, but there's nothing to do for them either way.
I also don't believe the world's population would suddenly drop if this were implemented worldwide. We're talking about assisted suicide, not death upon request to anyone who asks. The conditions are so strict, it's only intended for specific cases and it excludes the whole range of suicidal people who are not mentally ill or who feel the need to ctb immediately. Not to mention, even if you're not approved you can still take matters into your own hands. This would just make it more peaceful and dignified. I don't see how the lack of this service could possibly be why the earth is overpopulated because if you want to die you'll find a way; it's just going to take a long time (unless you're lucky) to figure out an effective method, a lot of suffering every time you fail an attempt and often times agony if you only have access to brutal methods.