You make an excellent point about the pioneer assets, especially in German battalions and regiments. In the article at the following link, it is noted that engineers organic to combat units belonged to the branch of the parent unit (i.e. the men in an infantry regiment's engineer platoon/company would belong to the infantry branch, not the engineer branch). As such, they typically served as assault troops, and had limited "engineering" training (and capability). How this can best be represented in TOAW unit organizations is probably by use of generic Assault Squads.
OTOH, the divisional pioneer battalion had the more traditional engineering mission. This was true at the beginning of WWII; however in 1943, the German divisional pioneer battalion mission began to evolve more toward the infantry pioneer role. At this time, the TOE of the divisional pioneer battalion in panzer and panzer-grenadier divisions became very similar to that of the infantry battalion by addition of a weapons company with heavy mount MG-42's and 81mm mortars.
The following is also from the lonesenty website. It is from a WWII, US Army publication (Military Intelligence Service, Information Bulletin No. 18, June 15, 1942), titled "The German Armored Division". What's not mentioned is that the pioneer battalion had flamethrower teams assigned, almost certainly for assaulting prepared defensive positions.
Section V: ARMORED ENGINEER BATTALION
The armored engineer battalion consists of headquarters, 3 light motorized companies (possibly only 2 in some cases), 1 motorized heavy bridge column, and 1 supply park. The motorized companies have 4 officers and 183 enlisted men each, and are armed with 9 light machine guns, 153 rifles, and 34 pistols. The heavy bridge column comprises all the equipment and personnel necessary for construction of a bridge of 28-ton capacity. It has 6 officers, 184 enlisted men, and is armed with 1 light machine gun, 153 rifles, and 36 pistols. The supply park has 2 officers and 48 enlisted men, and is armed with 1 light machine gun, 36 rifles, and 14 pistols. The personnel and engineer equipment is moved in passenger cars, trucks, tractor trailers, and motorcycles.
45. The armored engineer battalion is able to follow tanks everywhere on the battlefield. In cases where not all the battalion vehicles are armored or capable of moving across country, only the armored engineer company of the battalion can be used in direct support of the tank brigade.
46. The task of the armored engineers is to provide the armored division on the march and in battle with the necessary facilities for movement. These include:
a. Seeking out and removing obstacles in the line of advance;
b. Clearing lanes through mine fields;
c. Marking mined areas;
d. Constructing crossings and bridges with improvised or standard equipment capable of carrying all vehicles of the armored division.
In addition, armored engineers cooperate especially in the attack against permanent defenses.
"A good plan violently executed now is better than a perfect plan executed next week."
George S. Patton