Should teachers accept late work?

How many teachers do you know who tell you that their least favorite part of teaching is grading? I for one totally agree. Wouldn't it be great if we could convince students to want to learn for the sake of learning and not because they were being graded? Every year I change my grading system, trying to make it mean more. But I can't seem to find the perfect solution. If I grade everything it gets overwhelming, but on the other hand if you don't collect it how do you get the students to buy into the activity? I get chills when I think of my high school teacher saying, "Oh that's just for you." My response (in my head) as a high school student "Seriously! You have got to be kidding me!" And then there's the attendance issue. If the student is absent all the time can they still pass? If they do the work on their own? They're missing valuable in class discussion and interaction but they understand the material...so how do justify their success? Do we rate a student based on a test or on hard work? In the workplace we get paid if we do the work. If I have one crappy lesson I still get paid. But if I am continually unprepared there will be consequences. Ultimately if I don't know how to do a good lesson, when it's time for my evaluation I won't be recommended to re sign my contract. So do we grade like an employer would grade? If I stopped showing up I wouldn't get paid. So if a student doesn't show should they be allowed to make up that work? What about late work in general. Don't we want them to learn the concepts? But are they really getting anything out of a worksheet that they do not in context with the lesson, weeks after the lesson was taught? Okay so what about social skills and participation? If you factor these into their grade then are you still giving the student a grade based on mastery of content? Is the grading system inherently flawed or am I just missing something? Honestly I just don't know! It's all such a muddle to me, I struggle to have an opinion either way. What I do know is that all I can do is try my best to make sure the students are engaged and learning every day in my classroom. Maybe one day I'll have all the answers. For now it's just modify and adjust. A little of everything, some classwork, some participation, projects evaluated with a rubric, some tests and quizzes, and even some social skills in the mix. Trial and error, until the perfect system comes along. If it does I'll let you know!