First, any site can be made to be secure. When you have a large hosting environment run by a huge corporation which hires trained monkeys, the servers typically do not get the kind of personal attention they should and things like security become less of a priority than they should be.
What's more distressing, though, is that the exploit was added AND NEVER REMOVED. I'm not sure which is worse - a site which has an admin who is simply not capable of fixing the issue and preventing future intrusion or a site which has an admin who just doesn't care.
Rewriting parts of sites to render functionally on older browsers is neither rare nor difficult. Lots of people are having their sites redesigned to work properly on iPhones and other small devices, and the sites are offering smaller page loads, too. This part isn't insurmountable. Heck, I still use links (which is like lynx) from time to time, and I think because of iPhones and the like MORE sites are working just fine. Only a neophyte makes a site which only has Flash content or which won't work without Java these days.
What really matters, though, is having an environment which is cared for and run by people who care. A typical hosting company isn't going to really care much beyond the possibility that they'd look bad if they don't make things run properly. They're certainly not going to care about the $10 a month they'd lose should a problem customer leave when they've got 10,000 other customers.
I'm not sure I understand the rationale behind the suggestion that people should use a site which isn't cared for and which has security issues - why would anyone want to do that when Cammy is putting in the effort to set something up properly?