Setting drinks on fire is a decent example that is alone enough to justify what I said. Some people care whether you pour over ice or put ice in the drink. Whether they can tell the difference is anyone’s guess. “Lace” is cocktail terminology for the last ingredient. Muddling is another example; you don’t muddle after you mix. Sugary syrups and other infusions definitely change a drink’s character depending on mixing order, many drinks call for being
less mixed so you get a different taste at the beginning vs the finish at the end.
You can also think about recipes and cocktail names; order does matter to the corpus of recipes and lore and creative naming of drinks as much as it may (or may not) matter to taste. I didn’t invent cocktail history, so it’s not exactly my place to defend this, but I believe it’s fair to say that there are lots of recipes that call for ingredients in a specific order, in addition to all the examples where order is clearly needed/used.