No, you don't have to be proficient in any job to look down your nose at it, nor do you have to give 100%. You don't have to do a bad job well at all. Why? For what gain? What does it get you? Sweet FA.
That doesn't mean that any job is a bad job, there are good jobs that people are over qualified for, that doesn't make them bad jobs. There's a difference.
I can give you an example of a bad job, bad employer - poor pay, poor conditions, no future, employer takes piss by continually cutting wages, doesn't pay on time, holds back pay for petty reasons etc. the list goes on. Yes people need work, people with limited skill and ability. There were a couple of young men with Aspergers at the above factory, they struggle to find employment that suits. They couldn't just go into any job so they were stuck.
I've read your post about your issue with your co-worker. It's not unusual for those that have been through university then onto masters etc to struggle. D. had a problem with young engineers, his copany took on those who had done well at university rather than those who had been playing with the tools. As a consequence they had a load of useless engineers that hadn't the first idea about the industry they had just entered.
Starting at the bottom isn't the same as a shit job. However, if you are in the wrong job then that's a different thing altogether. If you don't care about the job that's one thing but if an employer doesn't care about their staff that is quite different.
KK - I don't know if your co-worker just doesn't care or is struggling or what. They do need someone to talk to them if it is effecting your work.
It's similar to where I work. There are those that put themselves out to do a good job and those that can't be arsed. Some feel like the management just don't care.
Making a job better is often impossible.