Ok, just to be clear, a GS-13 is comparable to a masters and a GS-14 is comparable to a PhD IF you are using education as your sole means of qualifying for the position. I was hired as a GS-11, promoted to GS-12 after one year, GS-13 after another, received two qualified step increases the year after, plus a regular step increase. So in a matter of three years, I was effectively promoted six times. Once you are on a career ladder there are no education requirements.
In terms of GS-15, their pay goes up to 170k, so its not like GS-15 step 1 is the end of the road. Federal employees have also been receiving above-inflation pay raises and COLA adjustments the last few years.
So why would a good engineer work for the government? Honestly, if pay is your only metric you use to choose your place of employment, then I would not expect them to. However, as I have mentioned, there are plenty of people in the world who choose their place of employment based on many factors other than compensation.
Is government work frustrating? Sure. I'm sure the same can be said of for the engineer developing a CRUD application and has a shitty senior engineer overseeing them. Government work can also be incredibly rewarding and unfortunately, the majority of the time you only hear about the government failures instead of its successes. The federal government issues in excess of 500 billion in contracts per year...I assure you, there are successes in there and I have seen some federal agencies that have implemented acquisition processes and development practices that are competitive with some SV companies.