This was considered once and declined. Sturmpioneers are already charged with assaulting (StG, Concussion Grenade), fortifying (Pioneer), repairing (Pioneer), and anti-tank (Panzerschreck). Being made anti-cover / anti-building would mean this one unit occupies 5 roles in OKW.
So that’s kinda the point of the faction.
Let me explain, the OKW faction is supposed to represent extreme late war Germany (winter of 1944 and on).
During this time period, more than ever before, Germany was faced with a military that was becoming more and more polarized between the two ends of the spectrum of experience and training as well as equipment. On one end you have new units being rushed to the fight with almost no training due to necessity and often equipped poorly with just basic rifles and panzerfaust if you were lucky. On the other end you also have those units that had fought and gained experience over years and years of hard fighting on all fronts and some very advanced weapons as well, but only in small numbers.
Commanders of these forces had forces that had the experience and training and equipment to do any mission, and the manpower to back it up with the fresh troops. Unfortunately for them all of the experience, training and skill was all in the same place, the veterans. The new troops may have been ready and willing, but they didn’t have the training or skill to use the advanced weapons, that are in short supply anyways. So you do the obvious thing. You give the best weapons and hardest and most complicated missions to the veterans because you can’t rely on the new guys yet and are you really going to trust your best equipment to your worst troops?
Back to the game, we see this as the Sturmpioneers as the veterans who are over worked with repairing, fighting, anti building work and anti tank work. They’re expensive to show their relative rarity and are over taxed because they represent some of the overtaxed and overworked veterans. This can also apply to many other OKW units, but Volks vs Sturms is the easiest and best example.
Putting even more roles on Sturmpioneers is good for the factions theme and may actually be good for forcing diverse build orders instead of just Volk spam. If Volks can’t counter cover then they need to be backed up by Sturmpioneers. You can still maneuver and fight from cover defensively with Volks against some enemies but you’ll need your Sturms if you want to assault. (Hence the name “Sturm” pioneers.) The problem of Volks losing to Riflemen is also partially solved by just using less Volks and getting more Sturms. Say instead of going Sturms into four Volks try going for only two or three squads of Volks plus another squad of Sturms. Now that you’ve got two squads of Sturms maybe you can afford to put a Shreck on one of them instead of a sweeper. OKW is a faction that has the most options and can do it all, if you can afford it. Cost is your limiting factor for them even more than other factions. Maybe this is a design flaw in the faction as a whole, so I guess if you want a more typical German faction you can always just play Wehrmacht/Ostheer.