In such a situation I'd be inclined to agree. I think my question is rather how many of the candidates for humane euthanasia would be in that condition if preventative healthcare was better.
Clearly there will be some people whose conditions could not be prevented by any medical intervention, but cuts to healthcare funding would probably result in more people getting terminal illnesses in total. Witnessing the suffering of patients is a big part of reminding people why healthcare is important (which of course is why medical charities advertise in this way). Thus, personally, my chief concern is that compassionate euthanasia could end up hiding fixable problems in our healthcare system.