It has to do with what the people want to see. Happy Days was headed for "one and done" until the audience suddenly sparked to a supporting character named the Fonz. And the only thing that stopped the show from being renamed from Happy Days to The Fonzie Show (seriously, that was a plan - though I might have the title wrong) was Ron Howard and the others balked. Plus Pratt & McClain scored a hit with the Happy Days theme song so the name recognition was established. They did do a Fonz and the Happy Days Gang cartoon, though.
It's not a case of a character being "easier" to write. I'm sure there are more than a few TV writers out there who hated seeing a show "hijacked" by a character they may not have particularly liked. But if it's a matter of tailoring a show to what the audience wants to see and seeing a series head out the door after 13 episodes, it's an easy choice.
Of course as a series matures, the whole "star power" thing comes into play and you start to see things like actors getting producer credits and the like. And if a show becomes too identified with one character you run the risk of the show collapsing if that actor leaves. The jury is still out, big-time, as to whether Star Trek Phase II would have actually worked without Leonard Nimoy. More recently, CSI, while not collapsing, necessarily, has been struggling to find its way since its breakout character, Grissom, was written out. In rare cases the whole cast qualifies as breakout, which is the case with NCIS - watch that show to end very quickly if any of the core cast leaves.
Even the unique case of Doctor Who runs that risk. Although it's a myth that the series collapsed after Tom Baker left (the ratings remained strong for several years after), the series never recovered from Baker's departure because he had become so internationally popular as the Doctor. More recently the departure of David Tennant created the same problems when Matt Smith took over, and although Smith is doing well, and the series remains popular worldwide, you still find people who are able to spin the numbers to claim the series has faded since Tennant left.
Alex
