Perhaps you would apply the same logic to a family car, or the clothing you bought? Should they tax the value of your medical degree when you leave the country?

Yes.

Remember that in Germany you don't pay for University degrees. High education isn't just for a wealthy minority.

I would assume that logic is applied.

Exit taxes are generally applied as if the taxpayer sold all capital assets on the day of leaving.

At least in the US taxation regime (I'm unfamiliar with others), family cars don't qualify for a capital loss, and rarely appreciate. Clothing would be similar.

But it doesn't seem unreasonable that a country should want to be paid tax on unrealized gains as you're leaving. It would probably be more fair to wait until the gains were realized and then apportion the gains among the countries of residence, but if you're leaving, it's going to be hard to compel your participation later, so it makes more sense to do it as you're leaving.