Transfer function of a filter: where is my mistake?
You seem to be considering that each of the low-pass filters will be independent and their cascading will be as having
$$ \frac{V_{o}(s)}{V_i(s)} = \frac{V_{o1}(s)}{V_i(s)} \frac{V_{o2}(s)}{V_{o1}(s)} \frac{V_{o}(s)}{V_{o2}(s)} $$
But, unless you have buffers between each stage you do not have those individual
$$ \frac{V_{o1}(s)}{V_i(s)}, \frac{V_{o2}(s)}{V_{o1}(s)}, \frac{V_{o}(s)}{V_{o2}(s)}. $$
Take these high-pass filter and a resistor as example, individually they have some TF. But when combined they do not have the product of those two TF.