While in theory supporting more databases is better than supporting one, in practice focusing on MySQL has a number of benefits.
First, introducing support for databases other than MySQL would increase the testing load for all development quite a bit, as already the combinations of PHP versions, web servers like Apache, Lighttpd, and IIS, and Windows vs Linux cause a number of issues, multiplying that by an arbitrary number of database platforms is daunting.
Early on in WordPress’ history when DB abstraction was seriously considered we noticed packages like AdoDB were bigger than WordPress itself, which seemed like a lot of weight for little gain.
DB independence also requires far more than just dropping in a DB abstraction class, as basic assumptions WP makes about things like primary keys, indicies, auto incrementing fields, LIMITs, and more vary more from DB to DB than a class could support without serious code changes.
Finally, MySQL is ubiquitous and has shown to be fast enough and scalable enough for the highest traffic loads, so supporting other DBs would not improve the WordPress experience or our popularity much. As a feature request it comes up fairly infrequently.
All that said, every query in WordPress goes through a class called wpdb and that class can be replaced with your own by putting a db.php file in wp-content. So far this has been used for mysqli support and an advanced enterprise DB class called HyperDB, but in theory you could use that, and some wicked regular expressions, to add support for a MySQL-like database without any core code modifications.