It's not the existence of the second marriage, it's the bona fides that can be hard to prove.
For example, although there is no requirement in the law of Australia
for two married people to live together, Home Affairs (ie Immigration)
will look to the extent (although not necessarily the duration) of co-habitation
as one of the indicators of a bona fide marriage.
It's not the only indicator - there's a set.
ATO and Centrelink use similar indicator sets when deciding
if two people are (or are not) a couple.
The issue is serial spouse sponsors - people who marry one foreign national after another
as a way to get the spouse on-shore.
Sometimes, yes, it is genuine relationships that fail.
But sometimes, it's a matter of marrying fraudulently,
sometimes in return for for money.
Or, sometimes, entering into marriages where it is not clear
that both parties are wholly willing.
Or, to put it another way... human trafficking.