Bolt actions are just fine for Timber. Leverguns had a boom of popularity, especially out East, in generations past, but those days are long over.

Generally, leverguns are chambered in low recoil, low pressure, relatively heavy bullet weight, fast anchoring cartridges, and are generally built with shorter barrels and are most popular with iron sights. So the overall package is lighter, shorter, and supposedly faster and easier handling in the woods. So they were popular in their time when a nice bolt gun might cost $400 and a levergun could be bought for $250-300.

Many, many drive hunters made their entire hunting experience by wounding deer, flinging snap shots at running deer with a quick cycling levergun.