A density operator representing a mixed state of n qubits grows as 2^(n^2), or a system with leakage into the second and third excited states grows as 4^(n^2).
For just 4 qubits, this would be a 4 billion complex numbers, so 8 billion floating point numbers.
Even this isn’t a time-domain solution, where you might in practice need to solve the Lindblad master equation.
This is all assuming we have a model for the noise, which in practice is highly non-trivial and very dependent on both the implementation of the qubits as well as their geometrical and material construction, and would take a good deal of science and engineering work to do accurately in a way that it reflects both control dynamics and a specific manufactured sample.
Yes there are solvers on the market in Python and Julia, but they don’t give you realistic noise computations for “free”.