The core issue here, as often, is that it pits ethical and economic concerns against one another. There has been a systemic choice by web/tech companies to prioritize maximum profit, often at the expense of necessary user support and compliance. Because of that, user support/relations are deficient and there is little accountability for what they're doing, even if, as we often read here, a tech company cancels user accounts, projects, or monetary accounts, without anyone or anywhere to appeal. Age verification presents the same problem. If companies maintained a professional, human-centered user relations function, they could implement a non-intrusive, real-time validation process.
If we were in the real world, with for example a barman needing an ID, that single person could confirm the age without copying or indefinitely keeping the ID card. The digital equivalent would be a decent support representative who could conduct a live brief video interaction to confirm a user's age, without even storing a copy of the ID, and who could even require the parents to be there with the minors signing in. That would address both the need for verification and the data minimization problem.
Yes, that would cost the companies a lot of money, but that would solve both problems at the same time: verifying the user's age and ensuring privacy. And guess what, the same person could also serve as an entry point for other issues that no one can really appeal against now, like the frozen accounts and other horror stories mentioned above. Yes, parental control is necessary, but it is insufficient. Zero-Knowledge Proof thingies could allow a device to validate parts of the process, but the possibilities of circumventing this are so enormous and endless that they look to me as completely insecure (and using a third party validating this adds another layer of trouble).
The most effective way would be to reintroduce a human element in the process, but we have already given up, because we are at the mercy of the web companies due to their free tools. The governments trying to introduce some ethics to those processes are not the problem at all, they should be commended for that. We are the problem because we accept that what should be the web companies' responsibilities is not being fulfilled because we don't want them to make less money as we would lose some freebies. That's on us, not on the laws. So the answer to "Why isn't online age verification just like showing your ID in person?" is : because we collectively accept it is not exactly showing our ID in person.
Actually, it is not quite the case: the most warmongering country in Europe was the UK since the 1600s (between 16 and 18 times depending on the criterias you use, a war declaration is way less a clear cut decision than you might think). They most often declared war to France, whereas during the same time, France declared war about 13 times (mostly to Spain, Prussia and Austria). There is no single source for those numbers, because some count invasions as war declarations, and some others don't, and some count wars against coalitions as 1 and some detail the exact number of countries involved. If you want to compare that with Germany/Prussia, they declared war about 10 times during the same time. And if you want to know which country was the most declared war upon, it was France (about 20 times), whereas England/UK was declared war to only 10 times. So it would not be far fetched to argue that it was mostly England/UK that was the biggest warmonger of the past.