What are the consequences of letting two identical rows somehow get into this table?
One consequence is, of course, wasted space. But I'm talking about something more fundamental, here. There are times when duplicate rows in data give you wrong results. For example, if you grouped by the int column (field), and listed the count of rows in each group, a duplicate row (record) might throw you off, depending on what you are really looking for.
Relational databases work better if they are based on relations. Relations are always in first normal form. The primary reason for declaring a primary key is to prevent the table from getting out of first normal form, and thus not representing a relation.