Another point worth considering, is that if we Euthanise the terminally ill, we lose incentive to research and actively combat those illnesses. If there aren't many terminally ill, why would limited research grants be used trying to stop the illnesses involved? Without institutions with such patients, they will be somewhat forgotten about or loom less large in our research efforts. There would also be a far smaller pool of people available for studies on the conditions.
To illustrate what I am saying, there is very little research being done on Malaria outside the third world, as it has been largely eradicated there. American Universities aren't studying TB as much, more diabetes and cardiovascular diseases. We study what morbidities we find in our populations, so if we artificially lower the disease burden in the population by Euthanasia, the incentive to address and treat that burden is also lowered.