The ASX would fight it tooth and nail - their biggest customers...

The ASX would fight it tooth and nail - their biggest customers (the brokers) wouldn't want it because it would make it harder (or at least a lot more expensive) for them to manipulate the market and fleece retail investors, and the ASX makes a lot of money from allowing the broker's computers priority access to the ASX's computers in front of "normal" traders such as retail investors so they can do their fleecing.

Some light reading:

https://www.abc.net.au/news/2012-04-11/kohler-high-frequency-trade-parasites-at-heart-of-asx/3943052

https://www.smh.com.au/money/investing/share-wars-how-the-robots-are-robbing-you-20120825-24t4t.html

https://www.smh.com.au/money/sharemarkets-rigged-by-trading-robots-20140426-37avz.html