The article "What is ... a Free Lunch?" nicely explains why market models with arbitrage opportunity are unlikely to describe financial markets of the real world.
Are there other properties of market models that are unlikely to be found in the real world?
For simplicity, let us stick to time-continuous models driven by Brownian motions.
For example, does the existence of two stocks $$ dX_1=r_1X_1 dt+ \sigma dW_1 $$
$$ dX_2=r_2X_2 dt+\sigma dW_2 $$ with $r_1\gg r_2$, $\sigma>0$ and independent Brownian motions $W_1,W_2$ contradict any common market axiom? There is no arbitrage-opportunity in this case, but my intuition still tells me that these two stocks cannot coexist in a realistic financial market, since I cannot imagine anyone that would buy $X_2$ if they could instead buy $X_1$. Is my intuition flawed here? If yes, are there any other signs of non-realistic market models?