Sure, but there are many areas of EE where demand has fallen. Programmable logic has drastically reduced the need for boards full of TTL chips. FPGAs, and even many ASICs, are designed with fully synchronous digital logic, that requires zero knowledge of most EE concepts, and can be done by any kid bright enough to master Verilog/VHDL. My company has done several successful FPGA projects, none of which involved anyone with an EE degree. ADCs, DACs, PWM, and DSPs come built into many microcontrollers, which themselves increasingly come on standard PCBs, with free downloadable libraries to handle all the interfacing.
And who do you think designs those things?
EEs are very much in demand, however they're not in demand for the old "computer engineer" or "programmer" style jobs.
Digital logic design still commands a small premium because it involves a LOT of advanced technology.
Though if you want to be in a field that's in resurgence, analog IC design is in. Even in the digital world - high speed digital signals behave in very basic analog ways that if your experience is in HDLs, you're not going to be able to figure out easily. Analog designers can command 6 figures easy, especially as modern PHYs are analog in nature, so you have to do mixed-signal ICs. Just because joe end user doesn't have to worry about it doesn't mean someone doesn't.
Then there's plenty of analog designs out there. A popular field is power engineering - you know, utility scale. Utilities all over the world are hurting because there really are only a handful of graduates in power engineering, not enough to replace the growing crowd that is retiring. (Yes, the flashy nature of computers and technologies have sapped the talent pool for other sub disciplines). Enough so that starting salaries are close to, if not above, 6 figures. Even those who want to retire are often asked to hang on because there's no one to replace them, or pass the institutional knowledge to.
There's plenty of RF work as well - WiFi and the like are easy to use, but that's because the RF guys made it simple enough to do. Even so, goof the design and you'll be wondering why you have limited range.