No, the general public should not have access to an individual’s criminal record. Someone who has committed an offence should have the right/opportunity to get their life back on track.
Depending on the nature of the offence, the conviction is eventually spent - this means it no longer has to be declared to an employer or voluntary agency, etc. However, for some convictions such as sexual abuse, or violence, these offences invariably stay on their record and would be revealed to employers, appropriate agencies, etc.
For women who may be concerned about the safety of themselves or their children from say, a new partner, there is the opportunity to make enquiries from the police department dealing with domestic violence or sexual offending.