The problem with what you have suggested is that most employees don't abuse the sick time and as result the cost to the employer is significant. For example, suppose I own a business with 20 employees and each employee gets 15 vacation days and 10 sick days per year. Assume four of those employees abuse the sick days and use all 10 for reasons other than illness, and the remaining 16 employees only use 3 sick days a year for days they are actually sick. The total number of work days lost per year to vacations/sick time is 398. However, if I eliminate the 10 sick days and give everyone 25 vacation days as you have suggested, then you can bet that all 20 of my employee will use each of their 25 vacation days, thereby increasing the total number of work days lost per year from 398 to 500.
OK, pick another number. I think most employees would be for it and it would protect their medical records privacy.