But a virus doesn't "spring to life." A virus is like a seed that just generates more seeds without ever making a plant.

The seed analogy may be onto something.

Some viruses don't directly cause the host to create new viruses. Instead they direct the creation of virus creating factories, which create the virus.

Then you get virophages which are even tinier than normal viruses, which infect the virus factories of other viruses.

When it takes over the cell, the cell is now the plant.

Seeds are not dead. Seeds are alive because their cells are alive. If too many of the seeds cells die then the seed can no longer germinate. That's why seeds can survive long periods of frost and stay active over very long periods, it is their cells that ensure they will be able to react to changes in the environment that suggest that the seed could germinate.

A seed is way more alive than a virus. It only needs very simple things.