From my experience most people don't use parser generator tools due to lack of knowledge that they even exist.
The first one isn't such a big deal for most programming languages, the second one is. Throw in better error handling and tricks like sub-file incremental and/or heuristical compilation (for IDEs), and the generators don't make much sense anymore.
I don't think you can make such a sweeping generalisation. Both JavaCC and Antlr have saved me a lot of time when doing DSLs in the past and both are well documented and easy to use. It would have been much more work for me to write the parsers by hand in Java. Both could also generate my own hand-rolled AST easily and so I do not see why integration would be a problem for most projects. I agree that generators do not scale to large compilers or projects with special needs, but that is not most projects.
Not so much when prototyping, when it isn't even clear if the language is going to get any users beyond the design team.
Everyone who is into compilers and parsing should try recursive descent at least once.