Assume that your utility function is
$$U(x,y) = \sqrt x + y$$
and your budget constraint is
$$p_xx+ p_yy = M$$
The Lagrangean is
$$\Lambda = \sqrt x + y + \lambda[M-p_xx+ p_yy]$$
and the first-order condition with respect to $y$ is
$$1 =\lambda p_y$$
We Know that $\lambda$ is the marginal effect of an increase in Income on the maximized utility function. So (considering discrete changes) if your income increases by $1$ kudo, maximized utility will increase by $1/p_y$.
It makes sense then to treat $y$ as the numeraire good, in which case its price is undetermined, our budget constraint is $p_xx+ y = M$, and the effect on the utility function by an increase in $M$ by one unit is $1$... as is the effect of increasing $y$ by one unit! But that makes $y$ equivalent to income, it is not "quantity" anymore, but value.
In other words, a good entering linearly the utility function is a natural modelling choice for a composite good that represents "all other goods", i.e. residual income after trading for the good $x$ we want to focus on.