Like any of us, I get a lot of request to review manuscripts from different journals. It tends to come in waves where I might go a month without, then have 4 requests hit my desk all at once. I would say that I turn down roughly a third of the requests I get, either because I am too busy with other things or because I already have a few sitting on my desk. Fair or not, I tend to decline smaller journals more often, usually because the science is less compelling to me.
But rather than just decline, I almost always send an email to the AE and suggest that they send the review request to one of my trainees. I tell the AE that I will assist my lab member with the review, but I don't have time to spearhead it myself.
People have asked me why I do this rather than just accepting and having one of my people handle the review. It's true that usually the AE does not end up sending the review to a student or postdoc. But sometimes they do. And when they do, the student or postdoc gets to handle the correspondence. They get in the journal's system as a reviewer. They get their name in the head of an AE who might see their good work and remember them next time they handle a paper on the topic. They get direct recognition.
I am not a PI who like to put my name on things my people do. I want them as first authors. I want my postdocs as PIs on grant applications. I want their name out there in the position that reflects their effort and I don't understand the motivation for making them ghost writers.