An RNA degradation plot doesn't necessarily make sense for the random-primer based arrays. Back in the day, the IVT step was based on an oligo-dT primer (meaning that the IVT step proceeded from the poly-A tail on the 3' end of the transcript) so there were two issues that could arise. First, there was the issue of RNA degradation, which may have 'chewed off' the 5' end of the mRNA, so you might be measuring partially degraded mRNA. IMO that wasn't really that much of an issue, because the probes for the 3'-biased arrays were really close to the 3' end of the transcript, and if you still had the poly-A tail, you probably weren't losing much on the 5' end either. The larger problem was that the IVT step only proceeds so far, and you might not generate much cDNA for the probes that were farthest away from the 3' end.
This isn't a problem per se, so long as the IVT step was consistent for all of the samples. But there is always the possibility that it was really poor for a subset of the samples and you would want to know that.
The random primer arrays, as the name suggests, use random primers for the IVT step, so you are generating cDNA starting at random spots in the mRNA. If the mRNA is degraded, you might get more cDNA from the middle of the transcript (IIRC, mRNA degradation proceeds from both the 3' and the 5' end of the transcript), but the 'early stopping' problem that could occur with the 3'-biased arrays has been solved by using the random primers. But since the IVT step starts at random places along the transcript, it's no longer possible to say if you had an 'early stopping' issue, because you no longer have a consistent start site for the IVT step.