No, of course there isn't an official expectation because the state doesn't interfere in our lives to that degree! (Not yet, anyway 😉)
But it's a reasonable human expectation that, if you feel uncomfortable around someone, they set your spidey senses off a-tingling, you have reasonable enough doubts about someone to suspect they might have a history of DV, then self preservation instincts would dictate that most people would naturally distance themselves from that person.
For many that instinct would be enough to end things, but if for OP it isn’t then she is probably the kind of person who should check.
Totally agree, which brings us right back to the start of the thread where the OP was questioning social services being notified.
Not ending a new relationship because your instincts didn't result in you automatically acting to protect yourself or your children, suggests a degree of vulnerability (which could be a result of many things!) and so that is why SS would need to just check a person's capacity for recognising future risk and further protecting themselves and their children.
As an aside, there are so many threads on MN where posters with no knowledge of the process tell an OP to 'do a Clare's Law check' on someone that I think some people regard it as little more than popping into your local police station and asking them to do a quick check on the PNC.
I think this has created a misunderstanding and people don't realise that what they're actually doing is initiating a legal process which involves both the police and social services and will be seen through to its natural conclusion however brief, long or potentially intrusive or whatever the outcome might be.