Adding scaled CRRA utility
You have to be careful when comparing different utility functions.
For example the function
$$
v(C_A) = - \frac{1}{C_A},
$$
and the function:
$$
u(C_A) + u(C_B) = - \frac{1}{C_A} - \frac{1}{C_B},
$$
cannot simply be compared. The first represents preferences over one good, while the second gives preferences over two goods.
So if you say:
$$
u(C_A) + u(C_B) &lt; v(C_A),
$$
you are in fact comparing two different utility functions.
If you want to know what happens if you only consume one of the goods, you need to compare, for example $u(C_A) + u(C_B)$ with $u(C_A) + u(0)$.
Also if you increase $k$ in the function:
$$
-\frac{1}{C_A} - \frac{k}{C_B},
$$
you are in fact making $C_B$ more valuable. To see this let's compute the marginal utility of $C_B$ relative to the marginal utility of $C_A$:
$$
\frac{MU_B}{MU_A} = \frac{\dfrac{k}{C_B^2}}{\dfrac{1}{C_A^2}} = k \frac{C_A^2}{C_B^2},
$$
which does increase in $k$. So the higher $k$ the higher the value of an additional unit of $B$ compared to an additional unit of $A$.