The Kanban columns can only be based on a Single Select field. The options in that Single Select field will represent the columns for the Kanban view. It needs a Single Select field because you need to be able to ensure that a record can only belong to one column at a time (only a Single option in the Single Select field can be selected for any given record), and also because it needs to know what your column titles will be (the names of your Single Select options).
None of the other field types offer that kind of structure on which to base a kanban view, so that’s why you need to have a Single Select field.
More info here:
With the Airtable kanban view, you can visualize your workflow in a board of stacked cards. Click and drag to move cards between different stacks, or reorder them within a stack. For a general over...
You have fields like link to another record fields where you can limit the selection to one. These should be included as well. Having single select or by assignee is too limited.
Already making that view type redundant for us.