Would you go through all the trouble of joining the Thieves Guild if its just to make a living?
As LostScout said above, it's hard work chopping wood. Any sort of manual labor for that fact be it mining, farming, smithing, even being an apothecary is hard/tedious and often times dangerous work. I'd think that's motivation enough for those that decide to become criminals. Why work, sweat, slave, and break my back for some coin when I can swipe as much (if not more) for another person? Thievery isn't always easy, but it's often quick and rewarding...more so than standing at a block chopping wood.
Just because you're a thief doesn't mean you're a bad person. I can still feel bad about taking things from people but justify it away as somehow 'necessary'. Everyone's gotta eat after all. Besides, how much harm could it really do? You have just a lovely house, own just nice clothes, and likely own a horse or can at least afford a carriage ride from place to place. What's a few missing silver plates and bowls when you obviously have so much more to spare. It's not like I'm a bandit or highwayman holding you at sword point, "give me all your things or I'll kill you". I'm just dipping into your pockets now and then for some spare coin, liberating you of your excess.
Hell! I'M REDISTRIBUTING WEALTH!
...and sure, your silver items and fine cloths will only go for so much. Maybe I want to up the stakes. If I'm going to be nabbed and do time for stealing something then it damn well better be worth more than a few measly gold coin. How would I do that? I could teach myself to pick locks and be sneaky, but you know what? A Thieves Guild might have people that can teach me these things. Also, once I've pilfered highly valuable goods from those that don't really need them, what am I going to do with them? I can't just mosey down to the corner market or sell it to the next vendor I see. It's STOLEN after all! What I need is a Fence, and I bet a certain guild has those all over the place. Or atleast... that's the rumor.
And so what if I get nabbed. I'll just take a respite in jail. Sure the food svcks and the conditions or wretched, but I'll survive and make it out to have another go at it. Or I may just get lucky and make a clean break.
I read your original post in the light of storytelling and role play (ie character motivation). Perhaps I was mistaken.
All this talk about story, role play, and character motivations aside; no it doesn't make much sense to join the Thieves Guild if all you're looking to do is farm gold. Setting your character at the wood block and walking away will net you a boatload septims all while you watch a marathon of TV show reruns or do actual chores. Alternately you can earn a lot of fast money smithing/enchanting items and/or crafting potions, especially if you spend time earning certain perks. You could stand at the chopping block for an hour and probably turn out more cash than running a few TG missions, but I'd sum that up in two words.
Game Mechanics.
Your character will never fatigue, will never need to take a break to eat/drink/sleep much less respite, there is no danger of accidentally missing and chopping off your foot or injuring a leg because you're fatigued, and even though you're "over encumbered" you can still slug 300 units of firewood back to the vendor and turn it all in for serious money. Game Mechanics don't always make sense in RP/Story context and are there more for the convenience of the player.