Depends on where you are and what pests you have. My worst animal pests are squirrels and possums. I just trap and relocate. Since at least squirrels are very territorial, if you clear out a lot of squirrels in the spring, they don't reestablish themselves in the area until the following year. That is, it's not like bailing the ocean. Not sure about rabbits. I suppose I could build an enclosure like yours (nice setup!), but that's not very convenient.

If that six foot fence goes all the way around the lot, I don't think many wild animals are going to affect you.

I agree with Dan; provided that it completely encloses the yard, the wooden fence should keep out the larger animals. Judging from the photo, rabbits could still get in under the fence; but it would only require about 2-3' of chicken wire fence to keep them out... which you could step over to harvest. Or... you could attach chicken wire to cover the fence gap, burying the bottom to discourage animals from digging under. That would protect your whole yard, only climbing or flying animals could get in.

Ground squirrels, if you have them (or their larger ground-dwelling kin) would be the only reason I can think of to provide such a tight enclosure. They can be tough to deal with, I had a running battle with them when I lived & gardened in San Diego. There was a large nest on an adjoining property, so as fast as I could kill or trap them, more would arrive to take their place.

For the last 12 years here, I've use a combination fence in my rural garden; chicken wire low, with electric fencing above that to 6'. Overall, it has been very effective. Deer could jump over it (and did so once), but once bitten by the electric, they avoid it. A ground hog twice dug under the chicken wire, but placing a live trap near the entrance hole, I caught both within days.