The general public generally are not aware of these issues, unless dealing with it themselves for a while, with support from people who have been through it. That's why so many advocate groups have to work so hard to spread awareness to ensure families and individuals know what to do to protect their rights (I.e. question about and question DNRs for example). There will be issues I don't know about, but I know about the Mental Capacity Act issues and how difficult it is for there to be sufficient oversight and rigor to ensure the act is carried out safely, and how rarely that happens already. For Assisted Dying, capacity is central.
If MPs have the same concerns, to vote something they don't think will be safely enactable at the moment into law would be disastrous.
Even referendums are generally advisory and cannot make the Government act in a certain way, although they are usually followed. A YouGov poll is several orders less rigorous than a referendum.