Agree for time spent learning new frameworks and technologies (i.e. generalist self-improvement that will be applicable to many clients and is part of your advertised skill-sets), but I would disagree on the example you've given (encountering an obscure bug during development).

Isn't this kind of learning really a discovery process inherent to analysis and development?

To take an old anecdote of the engineer who charges $1 for making a chalk mark and $9999 for knowing where to make the mark - if you're going "off the clock" while you work out where to make the mark (i.e. debugging a library), are you then charging higher rates when you "know where to make the mark"?