The lack of large-scale Einsatzgruppen in the invasions of Northern and Western Europe was a consequence of the friction between the Wehrmacht's leaders and the SS Einsatzgruppen during the invasion of Poland. The military simultaneously feared an upstart rival as well as thought the SS's pacification methods undercut military discipline.
These SS troops existed in an anomalous position within the chain of command as they were both soldiers and an entity tasked to hunt down Germany's political and racial enemies. The rampages of the Einsatzgruppen in Poland caused a degree of consternation in the military high command. On 18 September, members of the Waffen-SS unit Leibstandarte Adolf Hitler executed fifty Jewish prisoners. Although this formation was under the command of the 10th Army, its Heer commander von Reichenau did not give the order for the mass shooting, and contracted is superior for clarification, von Rundstedt who in turn telephoned Hitler directly. Hitler informed von Rundstedt that these actions fell under Himmler's responsibilities and not the military's. Hitler had authorized the SS to take command of issues of security and pacification in the wake of the German invasion, a task that the SS heads Himmler and Heydrich were quite willing to accomplish. Although there was some discomfort among Heer generals about the morality of these actions, most notably Colonel-General Johannes Blaskowitz who filed a formal protest against the SS-led Einsatzgruppen's actions in Poland, most of the dislike for the SS's methods stemmed from the fact that they often fostered a spirit of indiscipline among Heer troops brought in to supplement the strength of these security detachments. There was little to no sympathy among the upper-echelon Heer officers for the victims of the SS's actions. Even Blaskowitz at a February 1940 OKH meeting framed his opposition to indiscriminate murder as something whose main victim was the perpetrators, because "inordinate brutalization and moral depravity that would very quickly spread like a disease through worthy German human stock." The Abwehr also sided with the Wehrmacht in this institutional squabble, adding to a further diminishment of the SS in the upcoming 1940 campaigns.
The recent memory of Hitler's siding with the SS as well as what the Heer generals saw as indiscipline among SS troops led to the exclusion of large-scale Einsatzgruppen within the later invasions of Western Europe. The Wehrmacht trusted its own security police units for this task of security and they were able to get their way in 1940 because of the seesawing power structure of the Third Reich. The RSHA was present in various minor capacities during the 1940 invasions through SD commandos and various other elements meant to proactively police elements like communists or anti-fascist exiles. The RSHA also did discretely form is own Einsatzkommando within the Waffen-SS divisions. These units were much smaller than the ones in Poland and their formation was kept secret from the military. But the exclusion of SS security troops was a blow to the prestige and power of the SS and one in which Himmler and Heydrich did not stomach very well. Adding to their woes, the military occupation regimes for Western Europe tended to be run by the military, and thus the SS could not assume a greater role in running the security matters of the Reich in this new zone of German influence. The SD presence in in these countries often had to go through back-door channels to increase its influence break out of its subordinate position.
The role for the Einsaztgruppen for the invasion were part of a larger pushback by the SS to gain a more prominent role in the expansion of German power. Thus the RSHA tailored its mission in the planned invasion to play up its strengths as a crack counterintelligence force that could round up civilians like H. G. Wells and other problematic elements. The low priority of Seelöwe among the military chiefs allowed the SS to play a larger role in its planning, but this was also reflective of the SS's larger bureaucratic counterattack against being sidelined in the grand 1940 invasions. This bore fruit in the planning for Barbarossa as the SS was able to position itself as the premier German agency capable of dealing with racial-political enemies. Moreover, the SS was also able to iron out the command problems that eased the Wehrmacht's distaste at having its military subordinates enjoy a great deal of independence.
Sources
Gerwarth, Robert. Hitler's Hangman: The Life and Death of Reinhard Heydrich. New Haven: Yale University Press, 2011.
Matthäus, Jürgen, Jochen Böhler, and Klaus-Michael Mallmann. War, Pacification, and Mass Murder, 1939: The Einsatzgruppen in Poland. Lanham : Rowman & Littlefield, 2014.
Wildt, Michael. An Uncompromising Generation: The Nazi Leadership of the Reich Security Main Office. Madison: University of Wisconsin Press, 2009.