Crackability of a software

for example i think that a keygen is not always possible, but, imho, a patch is always possible

that is not true brother.
In some cases keygen is the only solution, and in other you need a patch and keygen.

Every software is keygen-able if you understand the routine. put some times it needs a patch to remove server check,....etc

also some teams releasas only keygens like : Core for example
some release cracked like EAT