Securing the seed phrase is one area that we have not arrived at a generally accepted means of storage because of the sensitive nature of the information being stored. The challenge is that every means of storage carries a significant disadvantage. For instance, writing it down in a piece of paper and locking it away have the disadvantage of the paper spoiling over time or when in contact with any liquid. Steel plate also has its burden of safe keeping and the possibility of corrosion.
The worst option is what is being described in the incidence which is carrying the seed phrase about. I have seen several recommendations in this thread but some of them are not straightforward and it will be very bad to use a method that will become problematic during retrieval.
You are right about seed phrase storage it is big problem with no easy solution because information is so private. Every way you try to save it has serious drawbacks. For instance writing it on paper can lead to it getting ruined by water or just old age. Even steel plate can rust or be hard to keep truly safe. Worst thing you can do as you said is carry your seed phrase with you. Many ideas for storing them seem too complicated and you are right we need method that lets us get our seed phrase back easily when we need it. This just shows how hard it is to find simple and safe and dependable way to store this very important information.