Your counter-arguments are specious. Do you know regex syntax, or are you arguing from a point of ignorance? It's an important point to establish your bias.
It's not at all like code golfing. I'm not sure of your connection there. Why not complain about pointers or something else using the same argument?
Regular expression's compactness has nothing to do with poor variable names. A variable named c could be anything. The regex syntax is neither ambiguous nor vague. It exactly describes its pattern.
It's a DSL. So what if it is? Have you ever tried to do complex things in SQL? It's a big mess too. Making the same thing require more typing and more syntax doesn't improve the situation. Most people I teach have problems with regexes because they are not used to thinking in and designing patterns, not because the syntax is exotic.
It's easy to understand once you know it. Well, it is. Power tools are not optimized for newbies or for people unwilling to learn. I don't complain about Lisp parenthesis, but I do not mind the regex syntax.
If you don't want to use regular expressions, then don't. Use the string manipulation functions or parsers. Use some other tool. While you're busy with that, I'll be ten problems ahead of you because I'm not swimming against the tide or blaming the tools for the work I can't get done.
It's up to you how much work you want to get done. Find the tool that gets you there the fastest and learn it. If you don't like that, invent something better. Until then, stop complaining.