I absolutely agree that the state of the MH system (and the social-care system that would help children early enough to stop many many mental illnesses developing is parlous. Plus the whole aim of the disability support system is to get as many people off it as possible, no matter whether they need support or not. That's a bloody poor indicator for future application of an assisted-dying law and that in itself should give anyone very long pause for thought over assisted dying in the UK.
But to say that anyone with a mental illness should not be considered sound enough to make the decision is, I'm afraid, cruel and very patronising. It's the same as saying 'you have a mental illness therefore nothing you say should be counted'. There are people who are so very badly damaged with no hope of healing that the only graceful and compassionate way to support them is to allow them, as with others, a certain and effective way out of life. That may not have been the case for you, but it is the case for others. You do not have the right to generalise from your case to make a decision for everyone.
Yes, some people will be able to unexpectedly recover. Others will not, and by removing the possibility of stepping out of life, it is condemning them to a lifetime of sometimes unbearable pain. The results of someone trying to commit suicide, failing and having long term physical damage can be just appalling.
At Dignitas it takes months to arrange an assisted death for mental illness and it's only if it's intractable, long term and you have three separate psychiatric reports, one from your local area and two from Dignitas itself, several months apart. That seems an effective way of doing it to me.
The biggest problem with assisted dying in the UK is the lack of care generally for vulnerable people. It's sad and frustrating to see that this is what the UK overall voted for.