One reason this isn't usually done is that the notation is ambiguous. Does "a+b/2c" mean "(a+b)/(2c)" or "a+(b/2)c", for example?
It would be possible to make / act like Plain TeX's \over macro, so that you could use "{a/b}" to get the equivalent of "\frac{a}{b}", and so the two forms above would be distinguished by using "{a+b/2c}" versus "a+{b/2}c", but that may not be what you want.
Alternatively, you may want to consider using AsciiMath rather than LaTeX as your input format, as it does use / for fractions.