Why do that at all, in the first place. Do we need to "preserve" the random seed between restarts ? What would happen if we don't? Will the computer have 0 randomness when it boots?
This turns out to be a much deeper question than you might realize. I'll try to do justice to it without writing a textbook.
Basically: computers suck at randomness; when you have some true randomness (aka entropy), it's a good idea to hold on to it.
Let's assume that your computer doesn't have a hardware random number generator. (Modern Intel chips have the
rdrand instruction that taps into a hardware rng, but for political reasons, the Linux kernel doesn't use it.)
On boot, where does the kernel get pure randomness from? According to Wikipedia:
The Linux kernel generates entropy from keyboard timings, mouse movements, and IDE timings and makes the random character data available to other operating system processes through the special files /dev/random and /dev/urandom. This capability was introduced in Linux version 1.3.30.
So mouse, keyboard, and timing of harddrive IO events. Let's say you need entropy during OS boot (for example you start
sshd which needs to generate keys on its first startup), you haven't loaded the mouse and keyboard drivers yet, and that early in the boot cycle you won't have made very many disk IO calls -- hell, early enough in the boot the kernel is still running in a RAM FS, and even after that you may be on an SSD or flash drive that has very predictable IO times.
So back to your question:
What would happen if we don't? Will the computer have 0 randomness when it boots?
On small embedded linux devices like routers that boot out of flash memory (both the small home ones, and the big datacentre ones that power the internet), this is actually a serious problem.
For an awesome read on this topic, see the 2012 paper Mining Your Ps and Qs: Detection of Widespread Weak Keys in Network Devices which has the shocking finding that
0.75% of TLS certificates [on the internet] share keys due to insufficient entropy during key generation.