AMD's Zen arch is an 8 core die, and they get very high yields out of it. Even the downmarket parts mostly or entirely had 8 working cores before fusing off.
Intel's big 28 core parts are (at least historically) a huge single die, with very very low yields. They charge a huge dollar amount for the parts because they cannot afford not to — the manufacturing costs are very high. There is some speculation that this 5GHz part is actually a bridged smaller die design, like AMD's Zen platform. Intel's bridge design is called "EMIB," if you want to google that speculation further.
No. The 2700K was a high end consumer CPU that could be bought for about $300, and didn't need a crazy expensive motherboard or socket. It wasn't extreme (also note the lack of an "X" in the model name).
In order to maximize their yield and make consumer processors an economic reality, Intel tests every single chip that goes off the assembly line and cut the "fuses" of the regions that don't pass quality control. A perfect chip becomes an i7 (or an i9 or even sometimes a Xeon) while the less perfect chips become i5s and the ones with the most errors become i3s with most of their cores disabled.
As other posters have noted: that 2600K CPU part you bought in 2011 is the Intel Extreme line, which are the top of the line i7s that have not only passed QC on their cores but have also been "burned in" or tested for stability at the higher end of possible operating frequencies for that generation. You're literally comparing the best of the best from 7 years ago to stuff that just barely missed the dumpster.
For example, out of the dozens of desktops I've built for my friends, family, and me, all of the -K processors that I've used are still alive today - including an i7-965 Extreme that's almost ten years old now. My experience with i3/i5 is much worse.