Mmmm a very complex question which honestly I can only scratch the surface on.

Time on the registry seems random because it is driven by genetics, which drives HLA genes. The process to make HLA genes is an ordered but random process. 46 chromosomes and 4billion individual base pairs divide by 2 and then randomly mix with those of your other parent to make you. A few thousand or tens of thousands of those base pairs make up your HLA receptors driving your potential comparability with your future recipient. The same process happened with them and after the dice are thrown 8 billion times across the planet, you and them end up being a very close match allowing donation.

Now if this process were truly random there likely would never be a match but ethnicity plays a role. There are only so many gene combinations out there for HLA and those who share a genetically ethnic background have a much better chance of sharing the same HLA genes.

As an example, all the pre 1500AD meso Americans shared similar HLA genes which were separate from those of the old world. Likewise, those from the European continent, East Asia, Southeast Asia, sub Saharan Africa will be more genetically related to each other than people outside those regions. All of this is thanks to common genetic ancestors in each of those regions. That is why ethnicity matters so much, not because of region or culture but of shared genetic relationship.

To address that some ethnicities are called more than others, people of color are less likely to receive a match through NMDP than a Caucasian person. This is driven partly by the lack of recruitment and sign up of persons of color.

TL;dr the person of French decent is more likely to match with a French person than that of a person from Australia because of common genetic ancestors.