The definition given is the one actually used by scientists. It is the one used in scientific papers, and in day-to-day scientific work. The definition given to the public is no different, except the public usually gets a simplified version. (I have given a simplified version. Mostly, I skimped on the strange special cases, like viruses.)
This definition is also the one used in many Creationist books. For example,
"The small variations in organisms which are observed to take place today . . . are irrelevant to this question, since there is no way to prove that these changes within present kinds eventually change the kinds into different, higher kinds. Since small variations (including mutations) are as much to be expected in the creation model as in the evolution model, they are of no value in discriminating between the two models."This and other quotes show that many Creationists use essentially the same definition, although they may call it something else, such as "variation within a kind". Clearly it's a useful concept, that should have a name.
Morris p. 5
Some people would like the definition to bring in speciation. And, above that, ideas about how species are related, and common descent, and how various transformations come about, and about how much change is possible.
A definition like that would be a disaster. Dragging in huge omnibus topics would leave people unable to agree on the definition. They would need a vocabulary just to describe the definition - which would bring us back around to needing to name what I named "the process of evolution". And it probably brings in the actual past history of life, which has nothing to do with what a process is or isn't.
More significantly, my definition is operational. This means that it deals with measurable quantities, that are easily observed. An operational definition can be used when making quantitative statements about actual situations. It's useful to field workers, instead of being merely a subject of discussion.