I think that, whilst that is probably what will happen, it risks severely changing the whole way that the state pension is viewed.
At the moment, it is technically a benefit - of course it is, as it's money from people's taxes that is paid back to those considered in need of it (in this case based purely on age) - but it's generally seen as 'earned' in an overall sense.
With unemployment benefit, people hope not to be out of work and thus to ever need it. With PIP payments and costly NHS treatment, in an ideal world, people would hope not to ever need them.
But when it comes to pensions, everybody hopes to be able to do their 'stint' of working years and then be able to retire to enjoy life and the fruits of all of their hard work. Your pension is widely seen as your 'reward' and entitlement.
Many of those who have paid the most in taxes during their working lives will utterly resent the fact that they end up with much less of a 'reward' than those who haven't been able/have effectively chosen to pay in far less for several decades.
Instead of pensioners generally being considered as worthy and having earned what they have, and the suggestion of an older person who only has their state pension to live on eliciting sympathy and bonhomie from others, I can see people who get state pensions becoming considered as social pariahs, wasters, lazy, freeloaders etc. - the same way as many 'opinionated folk' blanket-view people on unemployment benefits already. Sadly, I think that there will come a time when those on the SP will deliberately keep quiet about it and feel ashamed, rather than freely admit it as a badge of honour that they've served their time, as they often do now.