Peter
these are my thoughts on the matter
I wouldn't call a flat bed that is edged a raised bed.
Edging that does not retain soil but merely marks or decorates the edge is fine but that does not make a raised bed in my opinion.
A raised bed does not necessarily need to be edged. (although i have found that if you don't all your lovely top dressing and top soil gets washed off).
A question: At what point does a deep raised bed become a 'hotbed'?.
PIC Help could not get pic in how do you do that?
Here's a pic of my strawberry bed - this is what i think of as a raised bed. In this case the sides are made out of old planks the paths are just compacted soil and stones. The levels have changed over time the paths got lower from walking on it and the soil level in the beds higher by applications of humus and annual top dressings. (pine needles on this strawberry bed so it needs to be a seperate bed as not much else would take kindly to that).
I have cheated a little and posted my smartest looking bed

most are more mongrel than this one whatever i can get my hands on so planks (probably far too rotted to be used really) the end pieces of pine trees when they have been miled the edge is just bined but our neighbour passes them on to me, flat stones and i even had a woven one i made from chestnut wips but soil came through the cracks so pretty as it was out it went.
I did try to just visually mark the bed boundaries because i wanted to be able to change the layout more each year but I found that the top dressings and nutrients got washed away in the rains. The higher the planting areas got and the lower the paths got the more got washed away.
So these are my reasons for adopting raised edged beds:
1.to increase the depth of the soil, ours is thin over rock.
2.to allow tailored irrigation for each bed and its crops, to help conserve water(we have a limit).
3. to allow tailored soil improvements or top dressings in the rotation and beds. (soil is naturally acid and needs to be limed but only for some crops.
4.to avoid annual digging which, for light sandy soil like ours just turns it to dust.
5.to make crop rotation, weeding and harvesting easier
6. and finally so that when i go down to the producing terraces it looks like its all undercontrol and planed even when its not.
7. Our growing land is on a slope and the edging creates flat beds out of it; keeping everything in place and ensuring even water distribution.
For me these benefits outweigh the downside which is that raised beds are less suitable to the light sandy soil and dry conditions we have here, as raised beds have a tendency to dry out faster. However, the fact that the beds won't be dug over again helps to maintain the soils structure and by adding a new layer of muck and compost twice a season we are able to increase the water retention of the soil with a little help from the earthworms; making it less prone to drying out. It seems to work.