Special case of 3DES 3DES uses EDE as it is backward compatible to single DES, but consider the following case $K_1$=$K_2$=$K_3$ which one is more secure EDE or EEE.
EEE with $K_1$=$K_2$=$K_3$ is measurably less insecure than EDE with $K_1$=$K_2$=$K_3$, because the former has 48 rounds, but the later reduces to just one encryption E, thus 16 rounds. Two consequences:


This makes brutes force require 3 times more rounds, thus adds about $\log_2(3)\approx 1.58$ bit of practical security against brute force (security in bits grows as the base-2 log of the computational effort); however that remains way too low, and was so even in 1999. Brute force is the typical attack against single DES, and works fine including for EEE with 3 equal keys.
This regains up to like a dozen bits of security that otherwise might be lost to cryptographic weakness of DES, beyond its low key size.


On the second point: assuming $2^{42.5}$ known plaintexts and as many DES, implementations of Mitsuru Matsui's Linear Cryptanalysis Method for DES Cipher (in proceedings of EuroCrypt 1993) break 16-round DES with excellent odds and thousand times less work than brute force, but not 48 rounds (and I do not see that subkeys of rank equal modulo 16 being equal can help much).

Note: Linear Cryptanalysis of 16-round single-DES could be the least computationally costly attack in CTR or OFB mode; but in many other modes, as pointed in comment, $2^{42.5}$ known plaintexts by itself allows recovery of a sizable fraction of other plaintext, thus linear cryptanalysis is impractical.