If you cut a key in half then the key strength of brute forcing the other half is reduced by half.
EDSA 256 bit keys has 128 bit strength security.
So if you cut it into two 128 bit "half keys" and the attacker has one it is only 64 bit key strength to resist an attack. While it may take some time and effort that is computationally feasible.
A much better option would be to construct the partial keys using XOR making each key have full strength.
I know what you mean, but to make it clear;
it is not halved, it is 2^128 times easier
