I still think some questions are being ignored.
The split classes is, I agree, a far bigger issue than INSET,or parents evenings, which are actually a fairly small proportion of time overall.
If a teacher of a core subject teaches a class for 8 of their lessons over a fortnight, and then someone else covers them on the teacher's day off, then I wouldn't want to be the person covering. It's a mugs game. You never feel you have ownership of the class, they are likely to achieve less in that lesson etc. Not fair on the pupils or the other member of staff.
And even though it's a lesser issue, what about INSET which is essential? Let's say you have two teachers jobsharing, one does 3 days and one does 2 days. What do you do when essential training falls on one person's day off? And to say something like child protection isn't usually given a whole day's INSET is missing the point - even if it's two hours, it's still going to happen on one person's day off. So what should the school do? Why should the school be disadvantaged by having to pay the person to come in on their day off? Money which would otherwise be spent on other things? The school would be directly disadvantaged by having two people sharing a job rather than one person, who will attend all INSET without needing to be paid extra. According to Tethersend, the argument here is that the school shouldn't agree to jobsharing in the first place. Well, that's fine, except you'd then have thousands of people who don't want to work full time, up in arms complaining about the school being unfair!
Do you see the point here? In very many cases, part time working is for the benefit of the employee, not the employer. And if people want to work part time, it's therefore in their interests to make it viable.
In cases where it's actually in the school's interest to employ a part timer, eg if there are only 3 days teaching needed in a certain subject, then I entirely agree, the employee should be paid for anything outside those days. But IME, and certainly in the schools I've worked in, the majority of part timers are job sharers or have negotiated a part time deal because it's what they want.