I think most technical writer/editors would certainly agree that maximizing one's utilization of "use" at the expense of "utilize" is an appropriate usage of one's attention to detail, along with attempting to minimize the use of "usage" in precisely the manner that this sentence fails to do.
Utilize is a common, ubiquitous, and standard usage of language, it is also a use of language that can be dispensed with in virtually every case.
Given, however, that "used" in other contexts is the opposite of "new," I don't think it can be safely said that in every situation "utilize" can always be replaced with "use."
It does seem also that there may be situations in which you are talking specifically about the creation of new purposes and/or methods for using an existing resource or the transformation of an idle, underused, or unused resource into something of new and practical use that makes the term "utilization" a better fit. In effect, if we restrict "utilize" to the meaning of "to make into a utility," then maybe we are on to something.
"How can we better utilize this running water? Let's tear down the waterwheel and build a small hydroelectric damn."
Still, it is hard to think of a situation in which "use" could not be used to equal effect. "How can we better use this water?" It really is the exact same question.
Even stock phrases such as "utilization rate" can probably be dispensed with in favor of "use rate." Is there really any difference, for example, between being "underutilized" and "underused"? "Usage model" can certainly be replaced with "use model."