They are numbered so that you run across such statements as "such and such a gene on Chromosome 15," so the question is whether this sort of locatability perhaps gives a chromosome its peculiar identity, even a raison d'etre.
The particular set of genes on a chromosome give it its identity, but there (mostly) isn't anything special about which genes are where. Big chunks of genes can be swapped between chromosomes without it having any real effect on the organism, or example.
But let me ask: Is this swapping a rare occurrence or fairly common?
Call it uncommon, although not extremely rare -- it happens in humans in something like a few births per thousand. It's not the norm, and is best ignored when trying to get the basic picture in focus. As someone pointed out, every rule in biology has exceptions (including the rule that all rules have exceptions).