"Maybe we should describe bacteria by their individual features and give that group a name"

We already do that. The function and genes of bacteria are what defines a bacterial species (or genus, family, or order). I do agree that the Wikipedia definition of "species" doesn't strictly apply to bacteria due to asexual reproduction and HGT. But it is still a useful tool for classifying bacteria.

Giving it a name makes talking about the organism easier. If I know that a person is infected with Staphylococcus aureus I know that the characteristics and treatment are going to be very different than if they were infected with Pseudomonas aeruginosa. Giving it a species name is a lot easier than saying they are infected with a coagulase positive, gram positive coccus.