Why was Buell important to the Civil War?

He was not very important.

To the casual student of the Civil War, his name is identified with inexplicable delays and missed opportunities.

His only act of initiative was to capture Nashville (against orders) while the enemy's attention was briefly engaged elsewhere.

He claimed that his (late!) arrival at Shiloh had saved Grant's reputation. But other Generals, including McClernand, also put forward various similar claims.

After his half-hearted pursuit of Bragg's retreat from Kentucky, he was removed from operational command.