I agree that life isn't fundamentally different from all other matter, but the reason we have the word at all is because it's handy to be able to encapsulate it as a reference class.
I think the reason we have the word is more to do with historical vitalism than with carving reality at its joints. These days it's most often, or at least most rigorously, used to indicate "that thing biologists study, with all the membranes and nucleotides and amino acids." If you want to be more abstract than that, I don't think trying to define "alive" is really a good approach at all, because it means too many different things. But you can certainly look at all the interesting things it can mean and figure out which one you're currently talking about. You might want to give it a new name, though.
Recently, Hank Green posted a video discussing the definition of life. He offered two definitions; that life acts in a manner to achieve a goal, and that life continuously decreases internal entropy.
There are problems with these definitions. The first definition includes every machine that has a function. The second one includes, for example, a machine that constantly reshapes parts of its body into a paperclip.
Other definitions of life are equally confusing, doing things like excluding viruses because they use other cells to reproduce, despite meeting the intuitive meaning we have for life.
So, dissolve "life." Why do we care if something is alive? To decide if its life has value. Hank dances around the issue, showing that life has no inherent value by using mouthwash to kill billions of bacteria in his mouth. But, he doesn't take this to its conclusion. It doesn't matter if something is alive or not. We won't suddenly care about the well being of viruses if a new definition of life comes along tomorrow pronouncing viruses to be living. What we value is sentience.
Bugs are extremely low on the sentience scale, so we feel free to kill them. Animals that are higher on the scale, such as cats, have laws preventing any sort of mistreatment.
tl;dr: Life is an ambiguous term, use sentience to describe a being's value.