Is home financing with 410K realistic and feasible for us?

It should also be mentioned that a BU pays only for a limited period if, for example, you are on sick leave for more than 6 weeks. It then possibly supplements the sick pay if the employer no longer pays.

Rarely have I read such nonsense, sorry. But "pub talk" fully applies here. If you can still work with chopped-off hands: fine. You should be clear that this does not necessarily represent the majority.
Other people here have also given enough examples (burnout, depression, etc.) affecting the "head." Incidentally, the "back," meaning spinal diseases, is now the most common cause of occupational disability. IT workers are even among the most affected here.
A teacher also works with the brain, and the number of teachers unable to work has practically shot up in recent years.

Every person's ability to work is the foundation for EVERYTHING in life; I cannot understand those who "gamble" with it. And those who start relatively early also get a reasonable contribution, for example, my partner pays 40,- monthly in her mid-20s for coverage of 1,500,- monthly pension. Since sooner or later every fourth person (trend rising) becomes disabled, gambling seems disproportionate to me.

On the topic of "coma": a private occupational disability insurance pays when you can no longer perform at least 50% of your current job. This is certified not by an official medical examiner but by one of your choice. I have three examples from my circle of acquaintances who are grateful to receive a disability pension, and they all still have their hands

Believe me, I have dealt with this topic enough. A disability insurance that gives me 2000€ monthly pension (which wouldn’t even be enough for me personally) costs me depending on contract details over 50€ a month. That’s too expensive for me! We went through all sorts of scenarios with our broker. There simply was nothing suitable. I have to mention that I pay significantly higher contributions because I work in a chemical company.
There are simply too many negative examples in my extended acquaintance circle. There, disability insurances were not paid because the lady (she was an assistant) could still work. She was paraplegic after an accident and could barely move her hands. After a long legal dispute, a minimal pension was paid out as a "gesture of goodwill." She could have smoked that for all it was worth.
Burnout often (not always) "goes away" after a certain time. Most are knocked out for about a year. Either the company covers this time or you cushion it with a daily sickness allowance insurance. My mother works at a health insurance company, and she knows of no case where burnout led to full occupational disability. So that doesn’t happen that often.
Depression … I don’t really tend towards that. Back problems … there are now plenty of ways to counteract that.
The only thing that would really be problematic for me are my eyes.

Those are MY reasons why I would never take disability insurance. It may look completely different for you. I prefer to take the risk and save the monthly money.

It should also be mentioned that a BU pays temporarily if, for example, you are on sick leave for more than 6 weeks. It then possibly tops up the sickness benefit if the employer no longer pays.

But it depends a lot on the BU. My husband's BU was not willing to do that. They even fired him after his herniated disc. Whether this is legal is currently being clarified by the broker. But just the attempt ... it makes me want to strangle someone again

I don't want to talk you out of your experiences and opinion, but they are at least very subjective. Especially the example of paraplegia is presented in a way that is simply too generalized. No - current - disability insurance will be able to deny payment for paraplegia in a previously healthy person. One would have to know many details for that, but let's leave it at that. I was and still am an incredibly strong critic of insurance companies, even though I myself worked in the industry for over ten years. I was never a salesperson, but a "questioner of purpose," yet I remain rock-solid convinced about one thing: disability insurance, private liability insurance, and for homeowners, building insurance are and remain essential. And I was able to gather many experiences over the long period, not only from acquaintances, where the positive aspects regarding payouts and gratitude outweighed. But BTT: realistic and easily doable

I agree. I am responsible for 80% of the household income. My wife would not even come close to my earnings. If my labor fails, we lose pretty much everything, even though we have little debt in comparison. Not securing that would be grossly negligent for me.

It should also be mentioned that a BU also pays temporarily if, for example, you are on sick leave for more than 6 weeks. It may then top up the sick pay if the employer no longer pays.

That is definitely not the case. The BU pays in the event of permanent inability to perform the profession. In practice, this means a prognosis of at least 6 months of illness/injury-related incapacity. The theory of insuring 2/3 of the net income because 1/3 would come from the state is nonsense. Berufsunfähig != Erwerbsunfähig. Furthermore, the BU is fully offset against other social benefits payable (Hartz 4, housing benefit, etc.). So if someone has insured 1000€ BU, after the insurance case they are not significantly better off than someone who lives on social benefits. Only the BU-insured person has paid a lot for it beforehand. A BU can make sense if designed correctly, but in many cases it only benefits the insurance companies.