Question: Out of curiosity, why does it often take *seconds* to obtain network configuration via DHCP when the CPU is capable of processing millions of operations per second and ping to the router takes a couple of milliseconds?

In my home environment with one WiFi router and about 5 devices, it is not rare to see times like 5-10 seconds.

Answer: 
In addition to the actual acquisition of the DHCP lease from the DHCP server (which typically doesn't take very long), some servers will first ping the IP address it's about to hand out before it actually hands it out to verify that it's not already in use on the network - this takes a few seconds to time out. The client sometimes will do the same (again, to prevent IP address conflicts) which will add some more time. Then, on top of that, some clients will also register their DNS entries etc.
Two reasons (and solutions) I found when I wanted fast replies from my DHCP server. 

1) My DHCP did a ping of the address it wanted to allocate. This added 3 seconds delay. I removed this by changing the DHCP config to have a mapping for MAC Address to IP address. This is basically using DHCP to allocate a static address. This removed the 3 second delay for me.

2) I have an isolated network, however, you may get this at times. There was a DNS look up being done, which for me resulted in many seconds delay from getting an IP Address from DHCP. In the DHCP server config there were options for our domain and DNS servers. After removing DNS options and above change I got instant replies from the DHCP server. (\*\*)

These issues were what I found in my setup. Your milage may vary.

cheers

LB

(\*\*) If I had a penny for every time a failed DNS lookup caused a delay which resulted in a strange knock on affect which resulted in me scratching my head, I would have many many pennies.