Realisation of a passive RC low pass filter
Note that your desired passive RC network is really just the cascade of multiple first-order RC filters, each of which have the transfer function $\frac{1}{1+RCs}$.  By choosing the R and C values to use in each stage, you can place pole locations where you want them in the $s$-plane.

Here's the problem: recall that the pole locations occur where the denominator of the transfer function is equal to zero. Therefore, for a particular RC stage, its corresponding pole location is:

$$
s = -\frac{1}{RC}
$$

Note that this value is purely real. This makes such a topology infeasible for implementing a prototype such as the Butterworth filter. Its poles are located in a semicircle in the left half of the (complex) $s$-plane. Since you can only place poles on the real axis using your RC stage topology, you cannot implement a Butterworth network. You end up having the same problems with other types like Chebyshev or elliptic structures.

The solution is to use additional elements like inductors or amplifiers; these provide more degrees of freedom in the resulting transfer function to place poles at other places in the $s$-plane. That's why all the references you can find use them!