Another reasonable implementation would be for the government to accept payment in the form of shares of your company. Personally I think this is how all taxation of illiquid assets should be done, but I suppose it could get complicated.

As an immigrant to Germany, I've often made the observation that Germany frequently has a really severe implementation problem. So I'm generally very sympathetic to that idea.

That being said, I'm not entirely sure that's the case here, and this is often also brought up in the context of strengthening the inheritance tax in Germany. In both the inheritance tax and the exit tax, the inherent applicability conditions are such that the end result is that there simply aren't that many people in a situation where it actually has a measurable impact. For the exit tax, you'd need to find people who 1. want to leave Germany, 2. already started a company here, 3. that company grew large enough that the Wegzugssteuer would really be a burden, and 4. that don't have enough liquidity, or cannot raise enough liquidity by selling some of their ownership, to cover the tax. That ends up being a really small number of people, which always eases questions about the reasonability (Angemessenheit) of the law. And in the context of inheritance tax, there's the added point that there's a floor to its application.

As another commenter mentioned, even for those situations where the exit tax actually is burdensome, just as with inheritance tax, there are two really simple solutions: first, create a floor for the minimum valuation by which the exit tax is actually assessed, and second, allow you to "sell" shares to the German government as a means of paying the tax, turning the Finanzamt into a silent shareholder in the company. I think both of these would be substantial improvements to both the German exit tax and inheritance tax.