They're not soft. I can't speak for other nations, but ever since WW2 American combat wreckers have had armored cab sections protecting the crew and engine. We obviously don't uparmor the ones intended for recovery in safe zones, though.
Those are first line vehicles usually integrated with the unit they're supporting. In the British Army an Armored Regiment would have the maintenance workshop attached to them so they're a regimental asset. They'd have armored CRAAV's for recovery and specific warriors or 432's to transport the personal. However once you go further back in the maintenance chain it's all soft skin box bodies.
Albert Speer said the same thing that not enough parts were being manufactured, and he was in charge of the war economy. So I'll put a bit more stock in his take.
I don't want to derail the thread but Speer's takes should be taken with a huge grain of salt. The so called 'Armaments miracle' was more down to the earlier work of Fritz Todt and the later application of dodgey stats than to Speer. Todt had a habit of telling Hitler and Goering things they didn't want to hear, and giving the Army a realistic picture of the level of support the German economy could supply. Speer was much more of a 'go along to get along type'.
Wehrmacht maintenance policy was pretty well established, it was just commanders chose not to follow it. Additional spares production would have been at the expense of production of new vehicles. Spares packs take a lot of management and logistic resources to get them to where they're needed. Particularly when the front line is 2000 miles long.
Wehrmacht policy was for damaged vehicles to be recovered, and shipped by rail back to the factory for what was essentially remanufacture. On a strained logistics system this has the added benefit of utilizing empty rail wagons returning to the reich.
The Wehrmacht probably because they treated logistics and the ability to show any understanding of Germany's economic situation with contempt, just chose not to follow their own policies. Keeping parks of damaged vehicles close to the front lines where often they'd end up being captured.
Another example is how the Wehrmacht abused their recovery assets. For the Panther Germany finally manufactured enough recovery variants (about 400 of the 6000 panthers made). Yet units insisted on pushing what was essentially a strategic asset into the front line.
An exampled of how things should have worked was during the Battle of Arnhem. A company of Tiger II's were loaded onto trains in Hohne and shipped directly to Arnhem. A few broke down on the road march to the Bridge, two more were destroyed by the Para's 6 Pounders (the 6 pounders aren't shown in the Movie a Bridge too far but they caused carnage on Armor crossing the Bridge). They were in Arnhem for less than a week, helped win the battle. Then the entire company was shipped back to Hohne including the damaged and broken down vehicles.
That was text book use of the Tiger Tank. However if they'd tried that on the Eastern front some unit would have seized control of them and used them to destruction in some attritional battle they shouldn't have been fighting anyway.
Anyway if the Ukrainians are smart, then their focus with knocked out armor is to recover it and get it to a railhead then back across the border, where some Germans on a 32 hour work week in an air conditioned factory will get them fixed in a fraction of the time it would take the Ukrainians to demand spares, and repair near the front line.