Well, I suppose it would save money/time for the police, courts etc. I would imagine fewer women would come forward with allegations if they know it would only result in a fine at most (which would not make the victims significantly safer, as the man wouldn't be removed from the home, and would, also, harm the family finances not just the perpetrator); and for those that did come forward, I would imagine the length and cost of the process would be much less for an "administrative" offence and fine, than for a "criminal" offence and possibility of prison etc.
But I can't help feeling that it is also supporting the macho "strong man" ideal which Putin himself seems very keen on. I think when "stronger families" is talked about, what they actually mean is the man being "in control" of his womenfolk and children, being the unquestioned boss and being able to keep them in line by force if necessary. Which does seem to reflect Putin's political approach too; so perhaps by advertising this as the natural order of things at a domestic level, they are also subtly reinforcing it at the national level.