Primary/Elementary Pedagogy: What is the rationale for the absent '+' in mixed fractions?
Solution 1:
Subtraction.
The mixed fraction form makes subtraction, and possibly addition, easier to parse.
$$2\frac{1}{2} - 1\frac{1}{4}$$ is easier to read, write, and understand at this stage than either $2+\frac{1}{2} - (1+\frac{1}{4})$ or $2+\frac{1}{2} - 1-\frac{1}{4}$. Students at this age have not encountered the distributive property, and they may have trouble attaching the '$-$' to the $\frac{1}{4}$.
Negative values are similarly challenging.
I don't think that this is a good enough reason, but it's a rationale that occurred to me.
Solution 2:
In my opinion, there is no good reason to write "mixed numbers" without a "$+$" sign. When I teach college students or tutor high school students and notice that notation in their work, I insist that they retire that habit for both of the two reasons that you mention in your question.
Furthermore, it fosters the sense that an expression like $\frac{17}{5}$ is not a "real" fraction and that you always need to perform division to write it as $3 + \frac{2}{5}$. This is detrimental, as it obscures the obvious fact that $$ 5 \cdot \frac{17}{5} = 17 $$ by making it look like the less obvious $$ 5 \cdot \left( 3 + \frac{2}{5} \right) = 17. $$
Solution 3:
Well since we're being pedantic, $1 + \frac 1 2 \text{ grams } \ne \frac 3 2 \text{ grams } = \left(1 + \frac 1 2\right) \text{ grams }$. Also, the expression $1 + \frac 1 2$ is not the same as the expression $1 \frac 1 2$, the first is an addition of 2 rational values and the second is just a single rational value written differently. In algorithmic formal logic this sort difference can be quite significant.
Since this is an opinion question, I'll vote for the actual culprit being the common omission of the multiplication sign, which leads to plenty of other ambiguities.
Solution 4:
Discounting practical aspects and tradition, as mentioned in the comments, there are no advantages.
On the other hand, ambiguity is simply just a fact of life. Even within Mathematics.
http://en.wikipedia.org/wiki/Ambiguity
http://www.xamuel.com/ambiguous-math/