This is probably a case of selection bias, as since some of the most famous commanders have been Irish, does not necessarily mean this is unrepresentative, nor that they became commanders simply because they were Irish. You would need to break down all the commanders by nationality and then by relative populations, which is no easy task.

One related point though is that Catholics were not permitted to hold a commission until 1829 (or renounce their faith). Wellington was a Protestant so this was not an issue, but may have been prohibitive to the majority of the Irish population.