Thanks DannyHamilton for the explanation.

If all participants in the early days of Bitcoin used the distributed wallet software we wouldn't have this unusual spikes for the values 0 - 58 and the graph would look like this: https://ibb.co/b3GnBQb

And why doesn't the graph look like this?

When we take DannyHamilton's post and change Step 2, so the graph would look like the original graph:

• Step 1: Build block
• Step 2: Add nonce to header but set the LSB (1 btyte of the nonce) as a fixed value
• Step 3: Hash header
• Step 4: ...
  

If you have a fixed value for the LSB, so you have 3 bytes (256^3 = 16,777,216) that you can change to find a valid hash value.