This idea is not bad at all, if we keep half of the money in cash at home and the other half in the bank, it can be safer. Because sometimes we may face many obstacles in getting money from the bank, in this case, if we have half of our emergency fund at hand, we can do some work with it and during that time we can get the remaining half from the bank. This can certainly be better, but it is a personal matter, because there are many who do not think it is safe to keep money at home, because there is a possibility of theft, so it is a personal matter.
You are claiming that splitting your emergency funds between your home and the bank makes things "safer." But right after that, you admit that keeping cash at home constantly exposes you to the risk of theft. So, how can a plan like that be considered safer when it directly introduces the chance of you losing half your life savings to a burglar?
Having a lot of cash just sitting there, losing value because of inflation, and always stressing about keeping it safe - that just totally goes against why you have an emergency fund to begin with, imho.