What does the BBC have to gain here by saying "hey, Bush is alright!"

One explanation is that things are published for a number of reasons. In this case, this piece is possibly not designed to tell people what they should be thinking about, but to signal to particular groups that the BBC is a "serious" (or in textbook speak "a legitimate") organisation.

So it may not have a direct intended impact on domestic issues, beyond signaling that the BBC thinks that Michael Gove (or whoever) could well be "Minister for Culture" with power over the BBC licence fee after the next election.

In Wales:

what could that translate into on domestic political issues, especially as we approach elections?

That's a complicated one and my brain isn't up to it right now.

In Wales:

I found the textbook arguing that the media doesn't actually have that much influence on how people vote in elections (hmmmm) but what is does do with some significance is set the agenda.  So it doesn't tell people what they should think about a topic but does tell them what they should be thinking about.

Of course, "telling people what the topic is" can be a very effective way of telling people what to think. The issue that springs to mind is "inheritance tax." The reality is that far more people are encouraged to vote Tory on the basis that they will cut "inheritance tax" than are actually affected by it. It also sets the parameters of the debate. By focusing on a "tax cut" as an isolated policy measure you teach people not to think about the infrastructure that needs tax money to be built, etc.