After reading an answer on this site about some particulars of particle usage, I recently got a copy of The Structure of the Japanese Language by Kuno. It has been an interesting read, although the copyright of the book is dated 1973 and the last printing (as far as the copy of the book I have is concerned) is 1980.
In the chapter for "Place Particles" を、に、で, the author doesn't seem to include へ in even a footnote, which is strange considering there were forty something pages dedicated to contrasting は and が.
The usage of を, according to the book, is to indicate unidirectionality over a major portion or dimension of the noun, and に is to indicate that the goal of the motion is the destination, and they are not entirely interchangeable as far as grammatical correctness is concerned. The above usage of seems similar to を that I've seen elsewhere of へ.
I am curious to know:
How similar are を and へ particles in the above context?
Is を commonly used nowadays in the above context?
How long has へ been in use in the above context? I'm not sure how to find a good source on this, either.
Edit: An example from the book, using the (Nihon-Shiki, I think) spelling present there
a. miti o aruku 'to walk along the street'
b. miti ni aruku 'to walk to the street'
c. miti de aruku 'to walk on the street (probably back and forth, and across)'