Genesis makes it clear that one man, one woman, for life, is the ideal. In the rest of the OT it is seen that the real world is a bit more muddy and unclear than that ideal, and sometimes we have to work with what we've got.
Matthew 19:9 HCSB And I tell you, whoever divorces his wife,
except for sexual immorality, and marries another, commits adultery.
Matthew 5:32 HCSB But I tell you, everyone who divorces his wife,
except in a case of sexual immorality, causes her to commit adultery. And whoever marries a divorced woman commits adultery.
1 Corinthians 7:15 HCSB But if the unbeliever leaves, let him leave.
A brother or a sister is not bound in such cases. God has called you to peace.
These scriptures define exceptions to the marriage bond. When one partner cheats, the sacred bond is broken, because they have given to another what was supposed to be for their spouse only. The wronged spouse MAY forgive the one who wronged, but are not required to. The phrasing indicates that the wronged spouse is free to remarry, because sexual immorality is an exception, because it breaks that bond, as does abandonment by a non-believing spouse.
It could also be argued that sexual immorality could include other things besides adultery, such as porn addiction or cutting your spouse off without a compelling justification.
The following scripture seems indicative that it is better to remarry than to risk immorality, given the temptations involved.
1 Corinthians 7:2
But because of the temptation to sexual immorality, each man should have his own wife and each woman her own husband.
Some denominations don't see it that way, of course.
As for whether it is a matter for law.... the US legal system certainly has Christian roots, but is secular and not theological. You'd have to convince a large majority to agree to get it codified into law.
Personally, I tend to hold to what I said above... but I'll add that I'm not going be judgmental towards someone who bailed out of an abusive relationship, as I would not tolerate being treated that way for very long either.