I’m not sure that I would call the need to use Simplify a “problem”. It is certainly possible in a practical application to have two correlated Around’s. In such a case I wouldn’t want the automatic simplification.
In fact, I would consider the automatic simplification of Around[12, 2] + Around[10, 1] to be a potential problem.
On my system I get automatic simplification with no need for Simplify. There is also an example in the documentation
In[1]:= Around[1, .1] + Around[2, .4]
Out[1]= Around[3., 0.4123105625617661]
Gianluca: It’s when each of those terms are multiplied by an unassigned symbolic value where the automatic simplification does not occur.
Interesting, the two expressions are not totally equivalent when the variable itself is an Around object:
In[1]:= Around[10, 1]*X + Around[20, 2]*X /. X -> Around[1, 2]
Out[1]= Around[30., 44.77722635447623]
In[2]:= (Around[10, 1] + Around[20, 2])*X /. X -> Around[1, 2]
Out[2]= Around[30., 60.0416522091123]
In other words, the distributive law is not valid for Around objects.