The "attention" in ML is "what you should attend to," not "alertness." In the sentence "They crossed the <???> to get to the other bank." you need to "attend to" the <???> word to disambiguate "bank". If <???> is "street" then it's "bank" as in "financial institution" (most likely). If <???> is "river" then it's (most likely) "bank" as in "muddy banks of the Mississippi.
It's perfectly fair to replace "attend to" with "pay attention to," so it's not a fundamentally different definition of the word. But I think a logical first reaction to the phrase "Attention is all you need," could be to think that what's being advocated has something with "alertness" or "arousal" being a single value that's being turned up or down, which would be confusing and lead to wrong intuitions.