We consider a general class of singular control problems with state constraints. Budhiraja and Ross [Ann. Appi. Probab., 16 (2006), pp. 2235-2255] established the existence of optimal controls for a relaxed version of this class of problems by using the so-called time-stretching method and the J1-topology. We show that the weak-M1 topology is better suited for establishing existence, since it allows to bypass the time-transformations, without any additional effort. Furthermore, we reveal how the time-scaling feature in the definition of the weak-M1 distance embeds the time-stretching method's scheme. This case study suggests that one can benefit from working with the weak-M1 topology in other singular control frameworks, such as queueing control problems under heavy traffic.