Narrow definitions of natural selection

It's come to my attention that the "production" aspect of natural selection has come to dominate over the "elimination" aspect - in some popular definitions of natural selection.

For example, here's Wikipedia:

Natural selection is the gradual process by which biological traits become either more or less common in a population as a function of the effect of inherited traits on the differential reproductive success of organisms interacting with their environment.

...and here's M. Prakash (2007):

Natural selection is defined as the differential reproduction of genetically distinct individuals or genotypes within a population. Differential reproduction is caused by differences among individuals in such factors as mortality, fertility, fecundity, mating success, and the viability of offspring.

Here's Ehrlich, Dobkin, and Wheye (1988):

In modem evolutionary genetics, natural selection is defined as the differential reproduction of genotypes (individuals of some genotypes have more offspring than those of others).

In these cases natural selection is defined in terms of differential reproduction. Differential mortality is demoted to a mechanism producing differential reproduction. This is bad. The things that we observe are the product of both differential production and differential elimination. It isn't true that differential elimination only matters when it produces differential production.

The proposal that differential reproduction is what matters is implicitly proposing that we have another category of selection: for differential elimination that doesn't cause differential reproduction. However that's a farcical category. What are we going to call that?

Those who want to define natural selection in terms of differential reproduction have not thought things through. Their proposed classification scheme is dreadful.