The socket was 'special' only in the sense that its only purpose was to accept an 8087; it wasn't an unusual component. Adding this socket would be significantly cheaper than adding what would come to be known as an ISA connector. It's also good practice to keep the PCB tracks short, so placing the 8087 close to the CPU would be preferable to having it on ...
But why was the 8087 designed such that it needed a special socket?
Because the 8087 is a processor EXTENSION, not another CPU.
The 8087 has, except for a few lines, exactly the same signals and pinout as the 8086/88. The socket is, except for 4(?) lines, a one-on-one duplicate of the CPU socket. This includes signals that need to be connected between both ...
It is my understanding that many microprocessors used dynamic logic. The likes of the 6800,6809 and the 6502 used this.
This reference discusses one such technique:
One thing to note – the 8088 registers are made from dynamic memory cells – they have to be refreshed.
This was unexpected (at least to me),
Same to me. And I guess to anyone else as well. Ken Shirriff's analysis of the 8086 registers clearly shows that they are not dynamic, but static, using the same inverter loop as the 8080 already did (and essentially ...