Why triple encryption instead of split+encrypt?

[solman@MIT.EDU]

Why do people do tripple DES and *shudder* tripple IDEA
instead of doing some form of non-redundant secret splitting
and then encrypting with multiple keys.

For example, instead of triple DES, why not

A) divide the compressed plaintext into blocks of n*64 (where n=2 in the
   simple example, higher in the overkill examples)

B) Split each block into n parts such that:

     i)   The splitting can be reversed.
     ii)  During the inverse of the splitting each bit in the plaintext is
          dependent on several bits from each of the parts of the splittext.
     iii) The total number of bits in the splittext is the same as in the
          plaintext.
    
   The last point will make this form of secret spliting relatively
   insecure, but that's OK for this application (I think, this is
   really what I'm asking you.)

C) Now, for each n*64 bit block you have n blocks of 64 bits. Hook these
   together in n chains and encrypt with DES with different keys in CBC,
   CFB or OFB mode.

D) Unencrypt on the other end.

You can make the key size arbitrarily large and it takes much less time
than triple DES and its immune to meet in the middle attacks. So why do
we use triple DES?

If I am wrong about the security of point B-iii, am I correct that by
switching to a secure secret splitting algorithm and setting n=2, we
still get faster performance for the same cryptanalytical hardness as
triple DES?

Cheers,

JWS