Eureka makes no sense

When I first saw Eureka I thought I should make sure I start watching
from the beginning. There are many sci-fi shows I've watched get
really interesting in about the 3rd or 4th season on which I've missed
all the supporting details of the story. Eureka might turn out to be
one of these, but I think I'm going to stop watching now because the
basic plot makes no sense.

Okay, it's sci-fi, so I'm not complaining about any of the technical
details. What bothers me are the characters. Some of them have no
purpose for being on the show except that the show needed characters.
I have a problem with Carter, Joe, Alison, and Zoe.

Bill Steele...

It all makes sense from the point of view of the writers:

I don't understand why a sheriff and deputy with no technical
knowledge get involved in solving the side effects of so many weird
science experiments (usually looking to Henry for the real solution).

Bill Steele...

BubbaGump...

That's all true. The characters have decent chemistry when they
interact. I just think some of them need better explanations for why
they interact (within the universe of the show itself and not simply
because they're on a TV show).

The sheriff gives the story a point of view--the weird science as seen
by an average joe, which would be most of the audience. Often he comes
up with common-sense ideas that haven't occurred to the specialists, and
that makes the audience feel good. Also gives the scientists someone to
explain things to, so the audience can hear the explanations. Without
Watson, Holmes would have just solved everything and the reader would
never know how.

I don't understand what Alison's purpose is except to answer her cell
phone and follow Carter around.

Bill Steele...

That's about it. Love interest for the hero. The world needs its Lois
Lanes.

Anim8rFSK...

Hmm. That makes Stark Lex?

I don't understand why Carter's estranged daughter suddenly decided to
come live with him the same week he arrested her.

Bill Steele...

Appeal for the younger viewers, especially the Sci-Fi young male
demographic.

Anim8rFSK...

And she's Kara.

Basically, the emotions displayed by these characters are shallow and
meaningless because they have no reason for being on the show, and
since the sci-fi parts of the show aren't that interesting I'm left
with no reason to watch.