Schools don't operate this way. By law, students must be allowed to make up missed work if they have an excused absence. Illness = excused absence, as does attending a funeral, and other civic responsibilities, like being called to testify in court. Vacations to WDW are not typically a valid reason to miss school, unless they are part of a field trip. Disney actually holds a number of educational programs (called the Disney Youth Education Program).
The FAR more prevalent problem is that students don't do the work they missed.
Generally, teachers WANT their students to succeed, so they do just about everything they can to get students to make up missed work: extending deadlines, reminding the student, calling parents, and talking to counselors if the student has missed any important grades.
No teacher wants to be exposed to puke, snot, diarrhea, blood, or pus. Does anyone?
More often than not, symptoms develop over a period of time. A mild runny nose could be allergies. A headache could be simple dehydration. Dismissing symptoms is easier than arranging to keep one's child home from school.
If anything, the fault lies in the other direction. Employers don't make it easy for parents and teachers to take a day off from work. Employers, including schools, penalize employees who take too many sick days.
Think about it. When a teacher takes a sick day, they turn their whole workspace over to a complete stranger. Again, is anyone comfortable doing that?
Teachers generally care a good deal about their students, and their students' success. Student success = teacher success.
That said, I agree mostly with your last sentiment. Education has evolved. Online lessons are likely here to stay!