The small Westcott softboxes I have have an integrated metal ring to which the fabric and softbox supports are permanently attached. The flash mounting bracket then locks to that. For an example from one of their small softboxes, see Softbox 26 Octa. Or for their larger ones, they use interchangeable speedrings (for different studio light brands, or for hotshoe flash), and for these, the softbox rods slip into sockets in the ring in a way which is more secure than what it looks like your example does. See Westcott Pro 36x48 for an example, and for a closer look download the manual and look at the instructions for setup there. Westcott is just what I'm familiar with — I think most higher-quality softboxes will have connections like this. For another example, look at the instructions for Larson softboxes; there, there's a backplate with pins which connect to grommets in the fabric, and "corner hubs" for the softbox rods.
Westcott also has a series called Apollo which is a sort of softbox/umbrella hybrid, and these attach and are held like an umbrella would be. I haven't used these (or for that matter seen in person), but it also seems reasonably secure.
If you go for a softbox which doesn't have this kind of more-secure connection, there's always gaffer tape. The pro-style connection to the speedring takes a little bit of setup, and the built-in ring approach means that the softbox can't pack as small as it could otherwise, so I think the design you've shown is an intentional compromise.