MATLAB provides the option to use cond to calculate a different-norm condition number. According to the documentation difference between rcond() and cond() lies in their implementation. rcond() is more efficient of the two, but less reliable.
As for the choice of L2-norm as default output for norm() function, I think it has to do with the widespread use of L2 norm. For example, the Euclidean distance between two vectors, similarly the least square error problems also use L2-norm between predicted and actual dataset. Other types of norms are not as common and intuitive as L2 norm. Therefore it make sense to set it as the default value for MATLAB's norm() function.
