It's like writing Perl programs without ever using hashes: it is certainly possible, but why forgo the benefits of such a powerful tool?

Because some people find they get more benefit using other techniques. See Are debuggers good? for a long vitriolic thread on this very topic :-)

For example I personally find doing TDD a far more effective use of my time than spending time in the debugger. The mere fact that I need to drop into the debugger is a sign that I've fouled up earlier since I've obviously written code that is too hard for me to understand. The incidence of me using the debugger on my own code is as close to zero as makes no difference.

About the only time I use the debugger now is when poking at other peoples code and doing exploratory testing, or maybe trying out a one liner.