For most professions there is an incredibly long lag time between a drop in enrollment and a shortage of workers. If everyone immediately stopped going into EE overnight, it would take at least 4 years before there was any noticeable effect on the labor market as people already enrolled continue to graduate. Then for some time you'd still have a large pool of reasonably young people that would be regularly changing jobs - it might take longer on average to fill a position but they would still be filled, and in the meantime the slack would be taken up by other employees taking on additional responsibilities (which likely aren't too extensive when the missing labor pool is just from the entry level cohort) and older employees delaying retirement. Indeed productivity may even improve in the short term as no one is taking time out of their busy schedules to teach the next generation. Only after about 10-15 years would you start seeing a shortage that can't be compensated for as the youngest EEs are settling down and thus less open to relocation, older EEs can't put off retirement for longer, and the tasks left undone are too advanced to be easily performed by other employees. Of course at that point you get rampant poaching which drives up salaries but it also makes firms hesitant to invest anything in training new EEs as they'll be poached the moment they're competent - thus even if the salary increase starts driving renewed interest in the profession the pipeline never recovers. You soon have lots of new guys competing for the same low-skill work which drives down starting salaries while only the old timers can be trusted with work requiring even moderate experience. In another few years the last of the "original" EEs start retiring and with them incredible amounts of tribal knowledge are lost.

While that's obviously an extreme scenario and unlikely to ever happen with electrical engineers, it's not too far off from what happened to many trades like welding.