We are paying for the incredible bamboozle that is the phrase "Machine Learning." If we used computerized statistical inference instead and the phrase "machine learning" did not exist the attitude to people from investors to regulators, from customers, vendors, doom sayers and boosters alike would be vastly better taken as whole. Nearly everyone here knows mostly when seeing AI written or hearing it that it's a total…
There's been plenty of progress in the last 15 years re-interpreting many ML methods as regression (any optimization is a regression if you set up the right likelihood function). But many important results and techniques -- including today's ubiquitous deep nets -- originated and had successful applications way before they had statistical interpretations. They came from fields like compression theory, database design, or even biological interpretations.
The term Machine Learning was introduced to re-focus the field on a measurable objective: algorithms that improve with more data. The "Learning" part was not an abstract term to tug on your imagination, but included formal definitions of how algorithms improve that involved slightly fewer assumptions than statistical learning (which is a subfield).
This lineage isn't that important today, but that focus on how learning is measured is still the most important guidepost both for ML research and for sorting out marketing BS from realistic claims. Certainly, state of the art work using deep nets for tasks like NLP, image and video recognition aren't designed by reasoning about the statistical interpretation, or tested by applying typical statistical tests. Popularizing this work as Statistical Inference or Regression wouldn't give any added intuition and wouldn't really describe the way ML research proceeds, or how ML systems succeed or fail.