In my opinion, that's enough, but the taxonomists of the world disagree.

There are so many organisms that are obligated to have a host to survive. Granted, they mostly need one condition or another that the host provides, rather than invading its cells, but I much find the distinction between virus and obligate pathogen to be just one that is being held onto rather than one that is meaningful. I'm open to someone giving me a real definition, though I've never encountered one I feel satisfying.

Worth noting, my opinion on the lack of consensus for species is that there genuinely can't be one. Humans try to classify biology, but biology doesn't care. You can look at the clostridium or clostridioides clades or the bacillus cereus groups and see examples of biology laughing at us trying to name a species when there is so much intermingling and genetic transfer or so little genetic difference between "species". Dengue virus subtypes might be even clearer, though that's an example of what should arguably be four species being lumped into a single one. Also, why would a non living entity be granted living entity taxonomy like "species" or "genius"? I think that's a matter of convenience, but it does raise an eyebrow because viruses have evolutionary histories as rich as bacteria or animals.

Then there's the "there's no such thing as a tree" argument, that I personally subscribe to.

Long story short, between understood "convention", attempts at classification (taxonomy) that can only approach but never reach the truth, the complicated phylogenetic nature of the world - the fuzzy line between the same and different, and the general resistance to change, I don't think there's really a clear answer for what constitutes an organism and why. Again, I'm open for debate or education.