Is standardizing a modified AES a good idea? "Recently" the Ukraine standardized a new block cipher Kalyna, which according to the abstract of"A New Encryption Standard of Ukraine:
The Kalyna Block Cipher" by Oliynykov et al. (warning: the paper contains a lot of test-vectors) is basically a modified version of AES.

The high-level changes (to Rijndael) were described as "four new S-boxes, new pre- and post-whitening, a new larger MDS-matrix and a new key schedule".

What was the (likely main) reason to not standardize Rijndael or AES?

As a "bonus" / side question:
What was the (most likely) design rationale behind the changes being made to Rijndael?
The most likely rationale to change the AES design is political. It's a NIST standard, designed in Western Europe.

It's a bad idea! How much scrutiny has it received? Almost none. How much will it receive? Almost none. Bad idea.