As has been said before, a German "AK47 analogue" would have cause more problems than it would have solved. If you introduce a new weapon that blows through a new kind of ammunition at a faster rate than any other high caliber small arm of the time you cause yourself a number of problems:
1.) you now have to ship all new ammunition to the front and lots more of it. Even if you use a currently used round from another rifle, you still get the second problem now. And as has also been already said, the Germans had plenty of logistics problems, between their own shitty planning and the tendency of their railroads to get bombed into smitherenes by Allied airstrikes.
2.)As reliable and "soldier proof" as it may be, it would still require time for all of the soldiers being issued it to get used to and farmiliar with how to service and operate one.
3.) as great as it is, you still need to manufacture tons of them to replace all the older weapons that the soldiers were already using, this will draw much needed manufacturing capacity and resources away from something else.
4.)If it was made by the Reich, there is very little chance that it would be a real AK-47 analogue, because the Germans had this nasty little tendency to make everything incredibly over-engineered and overly expensive, which is the exact opposite of just what the AK-47 became known and loved for IOTL. In which case you get either a different version of the STG 44 or a german assault rifle version of the Thompson Submachine gun. Which is to say that it is an awesome but impractical weapon.