Like others have already said, it’s an accessibility nightmare. On the other hand, it’s not like this is going away anytime soon – maybe screenreaders could learn to understand and read some such “fonts” (e.g. bold/italic at least)?
If you want to use such an effect on your own website that’s probably the way to go (although I’d probably try to use real text in HTML and replace it with some CSS magic... or just use a web font).
For social media / forum sites etc, they should definitely add this. Make a plain text / accessible (user) name mandatory and a display name optional. And give end users the choice to show canonical name or display name.