The Invasion is interesting because quite simply the Clans did not have to be any good strategically, their momentum and tech superiority let them overcome any planning shortfalls. Later waves and Tukayyid specifically the arrogance of being able to just run over the opposition came back to haunt them . . . in addition to Focht exploiting the nature of Clan warfare. Its pretty easy to set ambushes and predict axis of advance when you know where your enemy is landing (agreed upon during bidding) and they have very specific, very limited objectives (agreed upon during bidding). Which is explicitly counter to IRL examples- commanders/armies have been known to change their immediate objectives if they run into too difficult a defense, instead probing the flanks to get around it or striking deep around the sides to force defenders to pull back or be cut off. Or the diversionary attack on the 'edge' of the main line of resistance intended to draw off reserves and initial air/artillery support manages to successfully punch through the line.
Instead the Clans tried to bull through to their objectives (hey diddle diddle, straight up the middle- Jaguar combat motto) because they did not respect their opposition (b/c GREEN troops) and what they had been doing had worked, so why change? No one ever taught them the maxim, 'the obvious path is mined.' Most of BTU combat up to that point was more akin to US Civil War or Napoleonic axis of advance rather than European WWII battle lines . . . Tukayyid was the first battle to change that afaik, the troop density of the divisions protecting the objective cities. We did get a few running battles (13th Wolf Guards & ComGuards tried to use the same canyons to flank), but most were the Clans trying to push through the defensive lines which does not play to the Clans mobility strength while giving the IS combined arms approach a better position in the field.