That is because it IS a "cheap" lock.
The lock barrel is actually made of "pot metal" AKA "zinc" which is a very soft material.
To get around the soft zinc and to "harden" the lock and make it not so easy to drill they have inserted a key shaped steel fake front.
In your case the fake front is turning separate of the actual zinc lock barrel causing a miss match between the two.
Not sure if really "fixable" but I would perhaps consider pulling the lock barrel out and see if you can remove the useless front..
Lock barrel my fit a bit sloppy without some sort of shim..
Removal of the fake front may make the lock easier to drill out lowering the low security of those locks a few notches into the dirt in the process.