Why do all SSH-RSA Keys begin with "AAAAB3NzaC1yc"?
The public key blob doesn't consist of just the numbers that make up the public key: it begins with a header that says “this is an SSH public key”. The repeated prefix encodes this header.

RFC 4254 specifies the encoding of public key in SSH key format. 


  The "ssh-rsa" key format has the following specific encoding:

 string    "ssh-rsa"
 mpint     e
 mpint     n

  
  Here the 'e' and 'n' parameters form the signature key blob.


The string is encoded as 32-bit big endian length followed by the literal string:

0,0,0,7,'s','s','h','-','r','s','a'


Encoding this sequence of bytes in Base64 gives:

AAAAB3NzaC1yc2E


The public exponent is also usually the same, so the common prefix is even longer. The bulk of the key is the public modulus, and that is completely different in different keys.