A search shows that after sweetened condensed milk was introduced to South America in the late 1800s they soaked cake in it. But it would seem that that is the basic taste of the sauce. If you want it thinner, add milk. If you want it thicker, add evaporated milk. Adding both seems to cancel each other out.
Well otherwise it would only be dos leches cake.
“I don’t always drink milk, but when I do…”
Sweetened condensed milk has a distinctive, slightly caramelized taste, the evaporated milk adds further milk sugars without adding as much additional fluid, and the whole milk adds the most moisture.
So you’re adding extra flavors, extra sweetness, and more concentrated options than you would be if you used just one of the above.
Otherwise, it’s like any other food preference - I have savory food options where I use dried garlic powder (in a dredge for example), crushed garlic (in the brine), and top with lightly fried garlic chips.
I’m adding garlic three ways, but it makes the garlic flavor pop Pop POP as Ruby Rod puts it.
Doesn’t make any of the three garlics, or the OP’s three milks redundant.
Tres leches? En esta economia?!
Localizada enteramente en tu cocina?!
That this was the first answer makes me proud to be in SDMB.
I assume someone wanted to soak the cakes (an old technique) in a milk product, and either didn’t have enough of whichever milk they wanted, or messed around with multiple milks to get the flavor they liked. I have to think the catchy name helped to establish it. And apparently “Nestlé played a pivotal role in popularizing the Tres Leches cake in the 1930s by printing the recipe on its milk cans.” (locogringo.com) sold in Latin America (thedailymeal.com), popularizing the recipe. (many other Internet sources agree on this.)
En esta epoca del año, en esta parte del mundo?
(At this time of the year, in this part of the world)