No. Although you could. Spacing too close together for most peonies except for the dwarf ones which are not intersectional. Too close together without air circulation means diseases will happen. Zone means nothing other than the temperature average for a period of ten years. Better to give your growing conditions as almost all zones can go from wet to dry conditions. From your stated desires it sounds like you should be planting herbaceous peonies not intersectional's. Herbaceous can be cut flush to the ground in the fall.

I treat my Itohs like herbaceous, have always cut them very short. We're in a zone where nothing above ground on them survives, anyway, so it's cut them down in the fall or cut out the dead stems after the new growth starts in the spring. I don't cut any of them all the way to the ground, though. Don't think that would be an issue unless your roots are planted very shallow and the eyes are damaged in the process. And my peonies are pretty densely planted but we're in high desert, don't really have any moisture related issues with them. Anyone living in a wetter area would definitely want to leave more room, depending on the variety. Remember the roots can span out quite a bit, you don't want them to crowd each other any more than you want to encourage fungal issues.

I would say be careful with the intersectionals. They develop short, woody stems at the lower ends and can also have new growth and flower buds hiding in the lower leaf axils. Any dead growth above that could be taken off.