Another consideration, if you are trying to get good DoF (as opposed to shallow DoF) at wide apertures, is resolution fall-off near the edges. Wide angle lenses are particularly susceptible to this at wide apertures.
When attempting to get a shallow DoF, performance at the edges is usually not a concern. But focussing at infinity, or close to infinity, with the purpose of achieving maximum DoF, I imagine that performance at and near the edges would be a concern. So basically, at F2, you could expect below par resolution at the plane of focus and very much below par resolution near the edges. Sound enticing?