Hello, I sought it best to post this response here under spoilers. Jarl Siddgeir of Falkreath seems quite wicked and greedy, desiring me to kill a group of bandits that are not giving him enough money. Now my character wants nothing to do with this greed, and would rather usurp those with similar mindsets. Is there any way I can avoid doing this quest, yet still become thane...and purchase the land to build a house (Hearthfire)? I hope the other Jarls aren't this arrogant...

You can join the Stormcloaks and have him replaced with a better Jarl. He's paranoid almost to a fault, but he's intelligent and actually cares for his people and wants to be a good Jarl. All in all he's much better than Sidgeir.

As Colonel said, the only way you can remove him is by joining the Stormcloaks.

Or, buy the land, join the SC, and remove him from power.

Id do that. Briefly help him, have him give you what you want, then remove him.

Both factions have a Jarl that really needs to have his head checked and acts like a little kid when he does not get his way, they also both have a mafia boss Jarl.

Imperials have Siddgeir and Maven respectively

Stormcloaks have Skald and Silver-blood (cannot think of first name)

Pretty sure you are able to help the replacement Jarl instead of the original to become thane if you want.