This is interesting - there's a DWP research report on exactly this topic from 2023:
https://www.gov.uk/government/publications/are-household-formation-decisions-and-living-together-fraud-and-error-affected-by-the-living-together-as-a-married-couple-policy
I haven't read the whole thing yet but the conclusion says:
(LTFE = Living Together Fraud and Error; LTAMC = Living Together As a Married Couple)
The increasing instability and plurality of family forms may make it more complex to delineate the couple and identify the benefit unit. A growing number of people are rejecting marriage or delaying it until later in life. Cohabitation is on the rise, whether as an alternative or a precursor to marriage. Cohabiting partnerships are on average more unstable than marriages, although this may reflect differences in the characteristics of people who chose cohabitation relative to marriage. A growing number of couples are living apart together (i.e. in separate households), for a variety of reasons. Increasingly, society is comprised of a diversity of family forms: single-parent families, blended families, extended families, etc. It was not possible to identify any evidence to link these sociodemographic changes to LTFE. However, these changes may make the application of living together policy more complex, and they may call some of the assumptions on which it is based (for instance, about financial support) into question.
The configuration of the UK benefits system may discourage some people from living with a partner and could theoretically deter people from declaring a partner to the authorities. The couple rate may deter some claimants from living with a partner, particularly if it expected that they will be worse off financially. People may also avoid joint assessment with a partner as a means of protecting their financial independence and autonomy. Research has highlighted the importance of financial independence to people on low incomes, particularly women. Claimants may not have (full) access to jointly assessed income from benefits, particularly if it is paid into a single bank account, as is the default under UC. These concerns are particularly important for claimants who have reasons to doubt the reliability of their partner – for instance if their partner is over-indebted; has a history of insecure employment; or has issues with drugs, alcohol or gambling – or who are in a new relationship. Undergoing joint assessment with a partner may be risky from the perspective of financial and other forms of domestic abuse, although further research is needed to substantiate this.
This is a complex policy area, with no clear or easy solutions. Different approaches are associated with advantages, disadvantages and trade-offs. LTFE ceases to exist if the household is no longer the unit of assessment. However, a fully ‘individualised’ benefits system would be costly and less effective at targeting resources at those most at risk of experiencing financial hardship. Steps may be taken towards individualisation without abandoning the household as the unit of assessment. In this regard, the UK might look to Australia’s partially individualised welfare system for policy lessons. The Australian system relies on a partner income test rather than a couple income test – an individual allowance is applied before the partner’s income is taken into consideration. Another form of individualisation would be to make split payments the default under UC or widen the circumstances in which these can be applied. However, this raises complex questions about how the award should be split across the two partners (50/50, reflecting roles and responsibilities or allowing couples to decide). The impact of the LTAMC rule on LTFE might be mitigated by allowing couples greater freedom, whether by introducing a transition period in which couples do not have to undergo joint assessment or by allowing claimants the autonomy to define their own relationship status.
I wonder if anything further was done on this.