Garlic will do fine with 4" spacing in a loose, fertile soil. Onions are probably better with 6" spacing if you want full sized bulbs, but can be planted with 3" spacing if every other one will be harvested early to make room for the others to bulb to full potential.

Dunno about leeks.

I did the exotic softneck garlic sampler this year with 4" spacing and they turned out great! Acropolis, Siciliano and Applegate stayed green the longest and they were quite large when I pulled them. Oregon blue was a weaker, smaller plant. I didn't get the others. Mabye be mine was a 4 pack?(One day I'll post this yews alliums crop in the gallery).I grew those and about 8 others in a 4x8 raised bed. I usually put my shallots cipollini in separate bed in part because I leave the shallots in longer, their roots might be more shallow, and they seem to need more water. Ditto the cippolini. OTOH, I think the shallots will be fine w/ 4" spacing, and the cippolini with 2". If you plant only a few cloves of each folic it could work.This is my fourth or fifth year overwintering various Cippollini & I've started to wonder if the time and space is worth the yield. They are "hecka" expensive to buy, but in a 2X4 block, I usually only end up with enough for one major recipe. MAYBE a pound. I didn't try choosing between alliums and tomatoes this year and both where in the ground in May. All the garlic where out my mid-June; the cippolini came outlast week and the shallots could come out any day now.