Here in Europe, we have had the UK and Italy actively pursuing rounding up migrants and deporting them to Ruanda/Albania until their claims are processed, and Australia has been doing this for decades now on Nauru and other places.
It isn't reasonable to expect countries to have a generous welfare system, accept all arrivals and exist on the same planet at the billion-odd people who live on a few dollars a day. Something has to give. I vote the welfare system but keep getting overruled; so one of the other two has to go. And we don't have the space tech to pick option 3.
For Germany, there is no legal way to enter the country if you're not caught by one of the larger dragnets (evacuation of personnel in Afghanistan, EU-wide assistance for Ukrainians and a few other rare international resettlement efforts). You are not able to apply for asylum outside of Germany, you cannot fly to Germany without a visa (the airline just won't take you as a passenger).
On paper yes you have the right to claim asylum. In practice, you have no way that doesn't make you commit at least one felony along the way.
People: [Let's go to Germany]
Germany: Get out.
People: How dare you round us up and deport us.
I know nearly nothing about German law, but I going by what you write if Germany doesn't make it legal to enter the country, then no surprise the people who try anyway run the risk of being deported. I have enormous sympathy for them, but the fact is Germany is famous for having a big welfare system. That means people can't just wander in.
Same in the US, you literally can't apply for asylum until you enter the country.
At least for America, many if not also the majority did just that... And then overstayed the time limit, which is a civil infraction in the same category as a parking ticket.
Republicans have proposed a special "come deport me" registry where not-signing-up is itself a felony, as a roundabout way to retroactively criminalize things.