Hi Jason,
Electroslag welding is the only process that has strict control on starts and stops (see 5.4.4)
One more mention is in Fig. 9.11 for K, Y, & T's
The potential for defects in starts and stops of a continuous fillet call-out is a real thing and you are right to think about them.
Since the potential for defects on starts and stops is real, and the code recognizes that. Performance qualification testing for fillets (see Figure 4.25) has a requirement for the welder to make a stop and restart in the center of the test assembly so that the required craftmanship or ability can be examined in a destructive test.
My opinion...... Since continuous fillet call-outs may be quite long.... Longer than you can sometimes expect a welder to accomplish without stopping or because SMAW electrodes force a stop; The code certainly cannot prohibit the practice of stops and restarts in fillets.