I have three characters that have attained commander or higher level. None of them have gotten an aid the planet mission since leaving Lt. Commander rank.
OminousVoice has had a similar experience as seen in the post made in that thread.
AzureAlliance provides some compelling statistics:
of 537 maps, only 26 of them have been relief efforts
4.8% of all exploration missions are relief efforts according to my data, so probably a 5% chance of drawing a relief effort is what's programmed into the game
While my thread is solely focused on Aid the Planet missions I think the stats and the topic overlap with the questions you are asking.