The burrow approach would not make it any less confusing. In fact, it raises even more questions. Right now farms function in a way that designates a plot to be tilled and upkept. How is that any different than the proposed burrow idea? The only difference is that instead of (b)uilding a farm, you designate it as a burrow and then all of your farmers can never leave that area because that's how burrows work.
Changing the farms to a burrow designation does absolutely nothing and changes absolutely nothing. Farms still need to be designated, still need to be tilled, and still need to be upkept. It would be far more simple to move farms into the (d)esignate menu and leave the options the way they are for the (b)uilding. Then require re-tilling every season. Bingo, farming is now more set-it-and-forget-it without having to fiddle around with burrows and assigning dwarves to them. Also, a further reason to not see any merit in the burrow idea is that this would invalidate setting farming labors. Setting the labors on your dwarves makes them do farm work. Why would I want to not only need them set to do farm work, but then also assign them to a burrow?
With a farm (d)esignation, you can assign a lever to be the "irrigation switch" so your dwarves can irrigate en-masse or you can simply leave them to muddy the fields by hand with buckets and water from wherever you have them getting water from. Furthermore, a designation would convey all of the fun balancing we want. We could implement growing areas for certain plants as well as water requirements (as dwarves would moisten the plants if required) and mud requirements. In farming designated areas, mud would never be cleaned up and any tile within that area would be considered fair game for planting.
Burrows are designed to give your dwarves areas they are and aren't allowed to go in in an attempt to streamline your workforce and eliminate them going to a meeting place a zillion tiles away. They are not designed to replace (d)esignations. Personally, I think most rooms (bedrooms, offices, barracks, dining, hospital) should be set via the (d)esignation menu. You then can look at them and see what furniture they require, how many pieces of that furniture are in the area, and which dwarf or dwarves the area is assigned to. Ideally this would let you make one big bedroom (bunkhouse) for your military dwarves. You could assign all of them (lets say 6. I like 6.) to the room and, if you hadn't furnished it yet, the display would let you know you have 0 of 6 required beds for the dwarves assigned and, if they request furnishings, 0 of 6 chests and 0 of 6 cabinets for the dwarves assigned.
The way I look at the system is that Burrows make sense like Dwarven Districts. You've got mining, industrial, commercial, agricultural, residential... Yadda yadda. Ideally we should be able to restrict dwarves from accessing certain districts while allowing them into others. Like if you separate your noble housing from your commoner housing, for instance.
Designations (or areas) means that "Stuff to do <x> goes here" where <x> is the designation. You're saying that this space is designated for this sort of verb. Eating, sleeping, farming, suturing wounds, drowning nobles. Whatever. Bedrooms, farms, and even workshops could fall into here. You could (d)esignate a "Forge" area and then place a smelter, wood burner, and metalsmith in it. Ideally you could, then, select the designated area and say, "Make me a pretty golden hat" and your wood burner would make charcoal for your smelter to smelt some gold ore and for your metalsmith to make you that pretty golden hat. If you wanted it encrusted, you could add a jeweler to the area and say, "Make me a pretty golden hat with lots of sparklies in it" and it would do that.
Zones mean that "This stuff is here. Use this stuff instead of stuff that isn't in this place." Like a pool/pond/cistern is a "drinking zone" or, as I call it, a "water zone". This means that water is here and tells your dwarves that you prefer them to get water from there over, say, the lake infested with skeletal fishmen. This can be used for sand, water, or even things you might do regularly like chopping wood or gathering plants.
Ideally, farming would be a designated area that would mean whatever you want it to. Lets say you designate an aboveground area for farming and it has boulders, trees, and shrubs in it. It should automatically designate those boulders for smoothing, the shrubs for gathering, and the trees for shopping. Then it should tell the dwarves to till the entire area if it's soil or muddy it if it isn't. I think, later on, it could be a good idea to allow dwarves to make gravel out of stone (so they are gravel floors) and then grind it with a millstone to make fine gravel, then mix it with mud to make soil that they can then use to cover stone tiles.
I think farming may require a different type of ground cover, anyway. Possibly differentiate between mud and soil. I think fungus (like plump helmets) should require one log to be muddied for them to grow on, as well. But one log would go a loooong way as many fungi can grow per log.
I'm going to drink more coffee now. I had two cups already. Workin on a third! Whoo!