It certainly has that default interpretation for me too, and if the attempt was not successful, then "I was walking to school" would probably be used. But I think "I walked to school" can be used in a similar way in casual speech when precision is not important and context clarifies the meaning. But you may be right that it "should" indicate success, whatever "should" means for language usage!
There's also a question about what "success" means here. For example, this seems natural to me: "This morning I woke up, then I walked to school, only to find that it had been teleported off the planet by aliens." Arguably I stilled arrived at the original location of the school, but it was gone. An interruption halfway there is less clear to me: "This morning I woke up, then I walked to school, only to realize that I had forgotten my backpack and had to return home". There the strong implication is that I actually arrived all the way at the school and had to walk all the way back, but probably in part because of context. Compare: "This morning I woke up, then I walked to school, but I got lost." That context clarifies that the attempt was definitely unsuccessful (unless further clarified that I then found my way again). But maybe that's because "walk to school" is a habitual action rather than a novel form? So what about "I walked to the new place, but I got lost on the way" -- that does sound strange, and "was walking" would be preferred, I think.