This seems impossible to fix in a divisional org structure, where each division owns their P&L. If I'm in division A, and division B wants something from us that won't make a difference on my P&L (or will just add costs [headcount]), why would I be incentivized to help? If they pay for it though, that's a fee for service. Seems fine. It's all internal accounting anyway, so it's mostly fake.
That likely depends on how exactly your org works. In my company, usually cross-org funded HC is permanent. It is expected though that you do whatever they ask for with that HC for ~3-5 years.
