Professional Web Analyst here. My day job is working with metrics on web sites. I'll try and weigh in.
First, we can argue and pontificate and philosophize all we want, but ultimately there is no proof of the pudding except the tasting. This is a falsifiable hypothesis. It can be tested, so it should be tested.
That said... I can see two potential issues with this metric.
1. It's a ratio metric. Whenever you metric by taking two numbers and combining them into a single number (in this case, by division), you are losing information. You are saying that several very different scenarios are basically equivalent. You are saying that your current density of 25 story links in a 500KB app, is basically indistinguishable from 1 story link in a 20KB app, which is also the same as 500 story links in a 10MB app.
It also means that there are two ways to "improving" this metric. If you want to double the current density of 5% up to 10%, you have two options: One is trimming the fat from the app so it takes up half the space. The other is making your stories twice as long. Your metric will not distinguish between these two cases. I'm not sure that's a good thing. In particular, having stories twice as long has no impact whatsoever on the homepage.
2. It's a "means-to-an-end" metric. If this metric is meaningful at all, it's because of the relationship to content load times and how much extraneous junk is on your homepage. But... you can just measure load times and homepage click-through directly, and optimize for those. This provide additional value beyond what those metrics give you. If anything, it provides less value by over-focusing on just two things, which is only one part of content load time, and is only tangentially related to design bloat.
If you've already decided that content load times are unacceptable and you want to make them faster, this is a metric that you can look at and it will make an engineer say "huh" and give you an idea of how much room for improvement it is. You can use it as a benchmark, and compare to other apps to get an idea of whether your design can be streamlined. But setting this as a top-level metric and optimizing for it is just as likely to lead you astray as to have a meaningful impact. And if your content load time is already acceptable, I don't see the value in what this brings.
tl;dr It has use as a secondary metric, if you've already decided to slim down your page, to compare against other sites and give an idea of how much you can improve. As a top-line stat, improving this metric does not have a strong connection to improving your app.