That is a very left-wing interpretation of why ANZAC Day is observed. And a viewpoint that very few in Australia or New Zealand would have expressed until, perhaps, the 1970s or so.
It may be difficult for Americans to understand given that the United States had to fight for its freedom from an oppressive British government in the 18th century, but Australia and New Zealand did not have the same negative experience of British rule that the United States did.
Australia and New Zealand gained independence and sovereignty as they wanted to gain it, at the time they wanted it. It was a gradual process that never involved significant antipathy to the United Kingdom.
ANZAC Day is important in Australia because it was the first time specially Australian troops went to war on any large scale level. It's that simple.
Was it a defeat? Yes, in the end it was. But it was a defeat that came within a context of wider victories. If the Gallipoli campaign had failed and the war had ultimately been lost, it's likely ANZAC Day wouldn't have much significance. But it became a symbol for the whole war in Australia.
It did not lead to Australians (or New Zealanders) coming to a realisation that we were sovereign nations for a few reasons. The first is that we weren't. We were self-governing in 1915, but we weren't sovereign nations until quite a long time after that. It's actually difficult to pin down when that happened because there's a number of contenders for that, but the earliest possible date, Australia could be considered sovereign is 1926 when it was agreed at the Imperial Conference in London that the 'Dominions' were no longer to be considered subservient to the British government, and it wasn't until 1930 an Australian government ever took a decision against the wishes of London. In 1931, the Statute of Westminster took effect in the United Kingdom, which gave Australia (and the other dominions) the power to act as sovereign nations, and it wasn't until 1941, that Australia actually did so for the first time - when it appointed its first ever Ambassador (to the United States) rather than just letting British diplomats represent Australia... that's the date I personally, would say, Australia became a sovereign nation, but some other historians would put it as late as 1986 - the point is, there was no moment that we just decided this was so, and Gallipoli had nothing to do with any of it. Australia remained proudly British for decades (separate Australian citizenship didn't exist until the late 1940s - we were British subjects until the early 1980s, and that only really changed then because Britain joined the European Economic Community (later the European Union) and Europe didn't want people from the wider Commonwealth becoming European citizens.