My question is very broad and general (and probably mostly unanswered), yet I would still like to hear your opinions on the subject, possibly alongside more reading material.

There is a large number of artificial life simulators available on the web (such as Darwinbots, GenePool and Simvidia) which simulate natural selection in a simplified manner.
A couple of things troubled me:
1. Eventually the population always reached an evolutionary dead end (either there was only one surviving lineage which stopped diversifying, or the population became extinct).
2. The evolution seemed deterministic, i.e the final surviving populations always developed the same anatomy when the environmental conditions were the same, even when the starting population(s) were different (or completely random).
3. The creatures didn't become more complex with time.

In the case of life on Earth on the other hand we see an enormous variety of anatomical features and survival strategies even in the same environmental conditions, with research suggesting that some evolutionary paths are not deterministic [Turner CB, Blount ZD, Lenski RE (2015) Replaying Evolution to Test the Cause of Extinction of One Ecotype in an Experimentally Evolved Population. PLoS ONE 10(11): e0142050. doi:10.1371/journal.pone.0142050].

I hypothesise that the difference lies in the simplicity of the simulations compared with the extraordinary complexity of life as we know it (e.g the simulated environment is too homogeneous, small and static while the genes and anatomy are too "rigid"). Are there serious attempts to simulate less "rigid" artificial life?

Why didn't life on Earth reach an evolutionary dead end? Is Earth rare in this sense?

you have answered your own question! you are absolutely correct when you say:
I hypothesise that the difference lies in the simplicity of the simulations compared with the extraordinary complexity of life as we know it (e.g the simulated environment is too homogeneous, small and static while the genes and anatomy are too "rigid").

I an not an expert in AI simulators but I would expect they would have to be improved by many orders of magnitude in terms of complexity to even come close to thousands of millions of years of evolution.

as to your other question:
Why didn't life on Earth reach an evolutionary dead end? Is Earth rare in this sense?

more correct to say it hasn't yet - evolution hasn't stopped and it could be argued that climate change will require it to speed up over the next millenium. Since we know nothing about evolution on other planets it is impossible to have a comparator to events on earth.