1- How often is an in-person visit to an academic library important?
R- Not all libraries are of books. there are some for toys, bones and taxidermy specimens, etc. Going physically depends on the type of library and what you want to check. Sometimes a book does not exists in digital form, so you have to go to a library to get the book and research what you need or even take the book out so you can digitalize it. Going as an act by itself it's irrelevant. What matters is why you need to even go physically... although libraries do have study rooms, in which case the importance is going to be able to use one of these rooms.
2- What means can normally only be accessed in-person?
R- depending on bureaucracy, you may need to go in person to get the library card, and obviously to take materials out and back home. In some cases also to make use of facilities (study rooms, computers, bathroom, etc) or services/activities (classes, reading clubs, tabletop RPG's, etc)
3- How important is to consider an institution with a good physical library?
R- Important for what? Consider for what?
4-Should a research group allocate resources for its members to visit physical libraries?
R- Depends on what they are researching. A research about ancient books needs to visit libraries, most other stuff dont even need their member to meet in person as it all can be done remotely via internet.
5-Can post-docs be hired at remote places which happen to have internet?
Question is weird and broad but the answer is yes as long as there is a remote work available like media manager or internet based stuff.