Short answer: Because the role exists and he was the least bad option.
Longer answer: For the most part, the political press doesn’t report news, it tells stories. Unlike most traditional stories, though, the political press ostensibly don’t want the readers/listeners/viewers to take a side. Thus–at least in reporting domestic politics–there aren’t “good characters” and “bad character,” they’re all presented–again, ostensibly–in ways designed to eliminate or at least obscure any bias. But stories without tension are usually boring, so media stories are crafted to create in the reader/listener/viewer a feeling of tension, of characters in conflict. The characters, their actions, their skill and their motives are usually presented in parallels. If a Republican says something crazy, for instance, the media will often ignore it, but if they do report it, they’ll also report some statement by a Democrat they they present as similarly crazy. If they present Republicans as “characters” they have to find Democrats who are similar. And it means that if they’re creating a role for someone of one party, they have to have someone in that same role in the other party.
Republicans have been growing less serious about policy for decades. (This, one of the best books I’ve read on American politics, is especially good on the decline of conservative thinking about public policy.) But when there’s a policy debate in Washington, the media does whatever it can to not present it in an unbalanced way, with good or bad associated more with one party than the other. This way it doesn’t get reported as “Democrats are serious–maybe too much so–about addressing budget deficits, while the Republicans are offering up ridiculous crap that isn’t taken seriously by anyone with a scintilla of sense and the ability to recognize utter nonsense.” They also don’t want to present Democrats in the role of experts on this or that aspect of policy if they can’t present a parallel Republican character.
This is where Paul Ryan comes in.
Yes, it’s true that Ryan has been cast in the role of budget expert because he’s the chair of the House budget committee. But he’s also cast as the Republicans’ “smart guy” and “policy wonk” in general; he’s their “ideas guy.” He is, of course, also either duplicitous or silly, because nothing he says or proposes actually is serious. But if stories about policy in Washington aren’t going to be presented as Democrats pushing policies and Republicans shamelessly trying to destroy the policies for pure political gain, regardless of the intellectual inconsistencies of their politics and the real-world damage the Republicans’ actions can cause, then the stories need to include the character of the Serious Policy Expert not just on the Democratic side, but on the Republican side as well.
In the House, even in recent years there have been some Republicans here and there who actually know something about policy and aren’t complete ideologues. They were called moderates, and they’ve almost all retired, been defeated, or–in the case of previously sensible people like Energy and Commerce chair Fred Upton–made the decision that it’s better to peddle bullshit and deny your actual beliefs so as to gain power and not incur the wrath of the far right that controls the Republican party.
Now, the Republicans’ loudest voices aren’t the ones with the most important thing to say. They’re just–like, say, Michele Bachmann or Louis Gohmert–the loudest voices. So what’s the media to do? Not tell stories? Well, sure, there’s some of that; they often choose to just not talk about substantive issues like budget negotiations. But when they do tell their stories, they need someone to be the Serious Republican Policy Wonk. Nobody who knows anything about the budget finds Paul Ryan believable in the role. But the media needed to cast the Serious Republican Policy Wonk,” and Paul Ryan was the best they could find.