How did the concept of "paid" vacation time and "paid" sick days ever start?

In the same manner as with award points you get with your credit cards. It started as a system to attract the right people with the right qualifications, and make them stay long enough to be productive in the workplace. You can either do this by offering them a better (or more competitive) pay, or you can devise a system or a package that offers them free time.

On the end of the day, an employer pays the "employee" because they need "their" services at the best possible price.

I don't know the history of it, but most employers are not "Scrooges" to their employees. Most want you to take vacation so you can stay productive. If you work all year with no time off, most people can get very burned out, which has a much more negative effect on productivity than allowing vacation time.

As for sick time, again, it increases productivity. How productive are you with the flu? Can you imagine how much productivity would suffer if you have most of your employees in sick with the flu? So if you allow them to take a day or two off when sick, it reduces the sickness in the work place since they are not coming in spreading their germs and viruses, thus increases productivity.

Plus, for many people, these benefits, along with health and dental, retirement, and other benefits, are just as valuable as the salary you make, and all are critical issues when looking for a job. I know if I was looking for a job, I would not accept a position with no vacation or sick time, even if it had a higher salary than another job that does offer it. So on top of increasing productivity, it also helps to attract better quality people to work for that company.

During World War II the government imposed wage caps across the country, preventing employers from raising salaries. To attract new employees, businesses had to come up with other ways to entice them besides giving them more money, so they started offering benefits like paid time off, employee sponsored health insurance, etc. Things kind of took off from there.

Doesn't it make more sense to take a position with a company that offers paid sick and vacation time than a similar company that doesn't?

Paid time off allows workers to budget more effectively and to have a life outside of work. I know, I know, these are TERRIBLE, SOCIALIST ideas for a conservative.

yes, it's an added perk to attract and keep good employee's.