Raspberries do fine without support in my
experience. They will spread via the
roots, so you will need to occasionally dig up some plants to keep them contained.
I've seen blackberries grown without supports. The key with these seems to be cutting back the primocanes - the vigorous stems that grow in the spring/summer and will have next year's fruit - to about 18". They will bush out and support more fruit on a shorter stem. To stop a blackberry thicket taking over you need to stop stem tips touching the ground where they will
root. Basically, blackberries can be done but need regular maintenance through the growing season.