If you want the test of fit in each group, then that is the simplest way, yes. But summary() displays the chi-squared contribution from each group, and if there are no equality constraints, then the df are divided evenly between those groups, so you could always use pchisq() to calculate your p values manually from a multigroup model.
Terrence D. Jorgensen
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam