How common is mandatory attendance-taking in college courses in US?
In the US there are actually some federal rules governing attendance keeping. Colleges must account somehow for students receiving federal aid, for example. That is a lot of students, as it likely includes those with government backed loans. While the rule doesn't seem to require that instructors keep a formal log, they are required to know who is attending and who is not. 

For example, Here is a sample page from a large US state university: https://uc.uiowa.edu/faculty/teaching-instructional-policies/student-attendance-absences.

Some states will, themselves, impose additional rules, as will some individual privately funded colleges and universities. 

There are a variety of reasons for such rules, including liability. If a student "disappears", especially one who is not technically an adult, the powers that be will want to know. 

Beyond such rules, some instructors count attendance in the grading rubric, but I don't think that is especially common post-secondary. But non-attendance can be a symptom of other problems and so instructors are expected in general to know who is there and who is not - especially when missing class or other activities is repeated frequently. 

So, while I don't know what percentage of colleges require this, my guess is that it is fairly high, based on the need to keep records. But it is also my guess that the rules aren't strictly honored in a lot of places.