I don't believe that the generating process for your simulation resembles that in the real world. If it doesn't, I don't see the value in such a simulation.

For an analysis of some situations where unmeasurably small correlations are associated with strong causal influences and high correlations (±0.99) are associated with the absence of direct causal links, see my paper "When causation does not imply correlation: robust violations of the Faithfulness axiom" (arXiv, in book). The situations where this happens are whenever control systems are present, and they are always present in biological and social systems.

Here are three further examples of how to get non-causal correlations and causal non-correlations. They all result from taking correlations between time series. People who work with time series data generally know about these pitfalls, but people who don't may not be aware of how easy it is to see mirages.

The first is the case of a bounded function and its integral. These have zero correlation with each other in any interval in which either of the two takes the same value at the beginning and the end. (The proof is simple and can be found in the paper of mine I cited.) For example, this is the relation between the current through a capacitor and the voltage across it. Set up a circuit in which you can turn a knob to change the voltage, and you will see the current vary according to how you twiddle the knob. Voltage is causing current. Set up a different circuit where a knob sets the current and you can use the current to cause the voltage. Over any interval in which the operating knob begins and ends in the same position, the correlation will be zero. People who deal with time series have techniques for detecting and removing integrations from the data.

The second is the correlation between two time series that both show a trend over time. This can produce arbitrarily high correlations between things that have nothing to do with each other, and therefore such a trend is not evidence of causation, even if you have a story to tell about how the two things are related. You always have to detrend the data first.

The third is the curious fact that if you take two independent paths of a Wiener process (one-dimensional Brownian motion), then no matter how frequently you sample them over however long a period of time, the distribution of the correlation coefficient remains very broad. Its expected value is zero, because the processes are independent and trend-free, but the autocorrelation of Brownian motion drastically reduces the effective sample size to about 5.5. Yes, even if you take a million samples from the two paths, it doesn't help. The paths themselves, never mind sampling from them, can have high correlation, easily as extreme as ±0.8. The phenomenon was noted in 1926, and a mathematical treatment given in "Yule's 'Nonsense Correlation' Solved!" (arXiv, journal). The figure of 5.5 comes from my own simulation of the process.