Actually, the "benefit classes", by which I assume you people who receive state benefits, don't get to live in accommodation "large enough to make reproduction viable".
They only get the local housing allowance (LHA) rate for the size of property they need, which allow one bedroom for:-
every adult couple (same or opposite sex, married or unmarried)
any other adult aged 16 or over (including live-in carers)
any two children of the same sex aged under 16
any two children under age 10
any other child
So you don't get a property big enough until you've actually reproduced.
And that LHA rate is based on the average of the bottom 30% of rents in the area, so in many areas you'll be lucky to find a place that's at or below that level. In my area, the LHA rate for a two-bed property is a tad under £1k a month, but it's very hard to find a property of that for less than £1,200.
And unless someone in the family is assessed and deemed to be disabled, the benefit cap means that they'll only get £1,666 a month, regardless of how much their rent is or how many kids they have.
I'd say that reproduction is pretty much not viable for the "benefit classes" in high rent areas.