"we know that inbreeding leads to deformed offspring"
No, we don't know that. (Or if we do, we have been misinformed.)
Consider Queen Cleopatra of Egypt, whose ancestry is well documented.
For five generations back, all of her ancestors descended from the same couple.
Most people have 64 great-great-great-great-grandparents. Cleopatra had only 2.
If that's not an incestuous family tree, I don't know what is. Yet no one says "So that's why Cleopatra was so deformed!".
Yes, if someone has a broken gene and their descendants interbreed, there is a greater chance that a child will end up with two copies of that gene. But the risk usually isn't high. When it does happen it typically means that that child won't have children of its own, thereby reducing the incidence of the bad gene from the gene pool. Except for the obvious case of the child itself, this is a good thing.
Here's an extract from something I wrote elsewhere about cousin marriages:
People's DNA has two copies of each gene. If one copy
happens to be non-functional, that's usually okay as the other will
provide whatever genetic information is necessary.
The problem is that if a common grandparent has a defective gene, two
grandchildren could each inherit that gene and both could pass it on
to their child. If that child has a gene where both copies are
defective, the child will have the disease, disability, deformity,
etc. associated with it. If the grandparent does have a defective
gene, the chance that a great-grandchild will inherit two copies of it
through their first-cousin parents is one in sixteen (6.25%).
Consider a common inherited disease such as Cystic Fibrosis. Among
northern Europeans, one person in twenty-five carries the damaged
gene. This means that the chance that a child of first-cousin parents
inherits both damaged genes from its double great-grandfather is
1/16th of 1/25th, or one in 400 (.25%).
Most inherited diseases are far far rarer than one in twenty-five, so
that .25% rate for C.F. represents an extreme case.
Now suppose we consider a rate of .25% to be too high a risk, and
use it to justify declaring such marriages illegal. What are the
implications of this?
If we applied the same criterion to Down's Syndrome, we would have to
make it illegal for women over 32 years old to conceive children, as
the percentage of 16-week fetuses with Down's Syndrome is higher than
.25% for 33 year old mothers. And perhaps we would have to make it a
criminal offence for any woman over 42 years old to conceive, as the
chances then are ten times higher than that.
Legally restricting conception based on the age of the mother is far
more justifiable than restricting it based on a first-cousin
relationship. But no jurisdiction has ever done that.