When you have multiple applications or instances writing to the database you will want all date/time references in the database to come from a aingle source -- the database server's clock. Otherwise you will be plagued by time zone and clock drift problems.

Another reason to use a TIMESTAMP or DATETIME type is you can use date/time operators and functions on it easier. For example timestamp_column + INTERVAL 30 DAY (in MySQL) is clearer than having to convert an INT.

Every relational database has more than one date/time type in case you only need dates without times, for example.