This manga is a damn travesty. Instead of asking the most fuckingly obvious question, "why not artificial insemination?", he does completely moronic stuff.
So does she, if she wanted to be secure and safe from rumors and potential problems and not being involved with any potential problems that might be caused by relationships, because let's be fucking real if you involve yourself with a young virgin chances are that he will develop feelings for you are above 90% i.e. it happens a lot, than artificial insemination is the most secure and safe way to go.
My point is, if author made such a crucial dumb mistake in a plot line early one what can we expect next, i already know the possible future points and fallouts, for example:
1) She will feel insecure due to their age difference which will lead:
1.1 To netorare like situations
1.2 She will push him away to "save" him
1.3 Situation where he talks(or went out somewhere) with a girl (brothers girlfriend or someone who isn't even interested in him) and she saw that and potential arc where she accuses him of cheating and they a whole arc invested in it
2) Some colleagues will blackmail them, why? Because either they will decide it to keep it a secret or company policy will be against it
3) Her actions will make him leave her (She will constantly state to him that it is purely until she gets pregnant and she doesn't feel anything for him), she will shove him away and then regret it.
4) Mysterious first love appears (hers) and tries to snag her only for our MC to try to safe her (least possible since the worst thing that Mysterious first love can do is pump and dump which is exactly what she wants)
In any case my biggest grievance isn't due to knowing potential roll out of this story but that the pillars that hold this story are already shaken by a major plot hole.........
The best option would be to make her ask him to become a sperm donor AND make their chemistry grow during the whole process and before the artificial insemination or after 1 that was unsuccessful they would decide to do it naturally since they got some chemistry going there. Hopefully author will address the problem with artificial insemination....Heck even a stupid reason like religious believe will do.