To wonder why we need party politics?

I've just been thinking about politics as they are now - Theresa getting into bed with religious fundamentalists to make a government;the labour party not all fully agreed on socialism; the party funding by corporations with vested interests; the braying and carrying on in the House of Commons. And I wonder what if we didn't have labour and conservatives?
Wouldn't it be better if every area elected an MP based on his/her viewpoints and then they went to Westminster to represent their area and form a Government who worked together for the common good of the people?
I believe that people go into politics for the good, and that they don't all agree on everything their parties say, so why can't they all work together without all this nonsense and corruption? What am I missing?