Hopefully someone can comment with specific Nazi policy on this issue, but I can say a few things about this on a conceptual theory level.

When you are trying to oppress and destroy a specific group of people, giving them large amounts of munitions is arguably the worst possible idea. The "undesirables" were heavily used for slave labor in building infrastructure where they could be closely monitored and denied food as a means of control. This accomplishes many pragmatic goals: starving people can't run or fight nearly as effectively as their well fed guards. Slave labor is wage and healthcare free (mostly). Keeping them isolated to camps and tightly controlled keeps them from being able to organize an effective resistance. Keeping them in the interior of the country prevents (or lessens) the likelihood of mass escape/defection and either directly joining the enemy or forming partisan resistance groups. Their labor is substandard in quality to a normal workforce, but still sufficient and worth it's price. This was where they could do the most "good" for the regime, at the lowest cost.

Now, let's flip the coin. Using "undesirables" as front line combat troops results in having troops with terrible performance as they have zero motivation to fight. It opens the entire military to a HUGE risk of sabotage. It requires a massive escalation of manpower within your armed forces that are dedicated to only watching/controlling these troops, rather than fighting or logistical support. It still costs just as much to feed/clothe/supply these basically combat-ineffective combat troops. This is where they could do the least "good" for the regime, at the highest cost.

However, the most important issue in my opinion is this: By including these peoples in the armed forces, you are legitimizing their value to your society. There is no way you can maintain a society of racial superiority if the "undesirables" are fighting and dying along with good aryan germans. You would be undermining your own ideology by giving a jewish/gypsie/black/homosexual/etc man the same uniform as an aryan man. You would be humanizing the undesirables to your civilian population, and would sow the seeds of social unrest in the politically moderate sections of your population. In short, you would be selling your whole social/governmental/national identity in return for soldiers worth literally nothing. It's important to remember that these undesirables were painted as being directly responsible for the hardships germany had suffered. What do you think it will do to the morale of your german soldiers if they have to fight and die on equal terms with such vermin? To see those rats in their own uniforms, eating their food, using their weapons? What about the logistical officers that have to direct food to these subhumans, food that should be going to proper german soldiers?

Now, the Nazi's did have penal battalions, which were comprised mostly of former soldiers in military prisons, and civilian prisoners. The important point here is that these penal battalions were made up of former soldiers still in active service, which means they would be entering the penal battalion already trained and could go directly into combat. After certain criteria were met they could potentially be effectively cleared of their charges and rejoin their former units as normal soldiers. This system only works because the penal soldiers have a goal to work towards. For the undesirables, what would be the point? They would never earn german citizenship, they would never be treated as equal human beings in society because german society was absolutely committed to the idea of racial superiority.

To end this on as simple a note as possible, the idea creates nothing but large-scale problems in every section of society.

The first thing to say is they actually used people who would be thought of as undesirable. Mischlings were often used as soldiers in the army and others who were more Jewish also served after been given essentially A free pass. One of the more famous examples is Erhad Milch who was a half Jewish Field Marshal in the Luftwaffe. Also if you were important enough even a full Jew could survive Fritz Haber the father of chemical warfare was born into a fully Jewish family and the Nazi regime wanted him to stay and help the regime. Haber refused and fled Germany. As for others it was considered that they were a disease on the German Race and would betray Germany the first chance they got. I am going to be now if you want further information I will post some more tomorrow