Perhaps a useful angle from which to look at this issue is to put it in the following way: towed artillery and self-propelled artillery are both mobile units, but they differ considerably in terms of their mobility, especially when one starts getting into the larger calibers. And a useful illustration of this fact is the situation that existed on the Western Front during WWI. For much of the war, the opposing lines remained largely static, even though men died by the millions trying to break through the enemy lines. Effecting a breakthrough was very costly in terms of lives, but it did get done many times; the real reason the war went nowhere in terms of gained ground actually had to do with what happened after the attacking troops initially broke through the enemy’s first-line trenches. Initial breakthroughs were effected in part by artillery preparation. Both sides mismanaged the tactics for doing this during the first years of the war, but got better at it later (when they realized that a short but violent bombardment was more effective than a bombardment that went on for days and days). After the initial breakthough, however, the advancing troops would “outrun” their artillery support and would come up against the enemy’s secondary trench lines. And that’s where the difference between towed artillery (which all WWI artillery was) and self-propelled artillery (which didn’t exist at the time) comes into play. The massive numbers of artillery pieces which had performed the barrage that had allowed the initial breakthough to occur took a long time to be taken down, hitched up, towed – especially over the muddy, heavily cratered terrain that their own bombatrdment had created – unhitched and set back up, giving the defenders ample time to reorganize their trench lines – or even to counter-attack and recover their lost ground.
The point here is that WWI mobile artillery, even though it was mobile, wasn’t mobile enough to allow the rapid exploitation of a breakthrough. By contrast, self-propelled artillery – even of the heavy caliber type – doesn’t just have operational mobility (which all artillery has, all the way up to the 800mm Dora railway gun which took a couple of days to set up for firing), it also has tactical mobility (which ideally can even allow it to “shoot and scoot”, as a tactic against counter-battery fire).