Why do we need to make simulation not only on baseband but also on passband?
So, we'll have to look at two things: Passband Signals and Passband Systems.

Let's start with the general notion that the consideration in domain A is equivalent to  consideration in domain B if there's an invertible mapping between A and B that covers all possible inputs and outputs of the consideration.

Signals

That mapping for the complex baseband and real passband domain for signals is well known; mathematically, it's the Hilbert transform, followed by multiplication with a complex exponential of negative center frequency of the passband.

In the other direction, it's the multiplication with a complex exponentionential of a frequency high enough so the complete baseband is at positive frequencies, and then removal of the imaginary part.

That immediately posts three requirements:


The Hilbert transform must be well-defined
There must be a center frequency for the passband signal
There must be a frequency higher than half the bandwidth of the baseband signal.


2 and 3 are equivalent, as far as I can see – you can only use baseband if your signal has been a passband signal before¹.

About the 1. requirement:

Tough one, I've been trying to generally state a domain of definition for the Hilbert transform, but that's nothing for a lazy Sunday noon. Concretely, and function $f(t)$ that fulfills

$$\left\lvert\int\limits_{-\infty}^{\infty} \frac{f(t)}{t-\tau}\right\rvert &lt; \infty$$

is Hilbert-transformable, and you need to account for the fact that you can use all your Lebesgue intergral magic here (you'll really have to, that thing usually has a singularity, and that is an example often used to motivate Cauchy's principal value theorem for electrical engineers).

Now, if $f\in L^p,\, p&gt;1$, then that's a given; but periodic (and hence, not-energy-)signals do work too; tempered distributions do, and a few other things.

Considering the fact that Parseval's theorem already tells us that, inherently, a signal that's limited in energy in frequency domain (and every band-limited signal has to be) needs to be in $L^2$, we can infer that there is none band-limited passband signal that you cannot equivalently observe in baseband.

Systems

This is the tricky part. We're looking for passband systems that we can't map back and forth from passband to baseband.


¹ – that's true for more than signals with closed interval support; compactness suffices, as far as I can tell, but your mixing function then is no longer a single complex exponential. For example, you could have an infinite real tone comb with frequencies $N\pi,\,N\in\mathbb N$, and your mapping to baseband could be Hilbert followed by multiplication with a complex tone comb $\sum_{m\in\mathbb N} e^{jmt}$, and would still end up with a proper baseband, and a way of converting that back to "strangely defined passband". But that's more about generalizing the notion of pass- and baseband than it goes to answer the question...