The main reason that sustained artillery was not a major factor in most World War I victories was that it was just plain ineffective. This is not to say that it was not tried. Artillery in World War I was used in a variety of ways, but they are broadly classified into creeping barrage and standing barrage tactics. True, with new artillery in 1914, a particular position could be surrounded with artillery fire that could be sustained, generally in bursts, for weeks. This was actually the tactic of choice during many conflicts early in the war, before the realities of trench warfare set in.

The idea of this sustained artillery fire fell into disfavour when it was proven to be largely ineffective, particularly throughout the Somme campaign (Zabecki, The German 1918 Offensives). Trenches are, quite simply, VERY effective defensive positions. With the kind of shells thrown around by 4.5-inch Howitzer or 18-pounder field guns, a properly dug-in position could weather those hits almost indefinitely (Ellis, Eye-Deep in Hell). By 1916, most Entente forces began using the idea of the creeping, advancing or rolling barrage. They would attack with artillery, quickly followed up by infantry. This was because the artillery fire had been allocated a different value: it was useful for suppressing the enemy, sowing confusion and causing them to retreat into their most defensive positions, prime for an infantry incursion (Marble, King of Battle). From this point, artillery was used largely in these creeping barrages or in standing barrages that became more formalised as “boxed barrages” used to keep the enemy at bay.

There is another tactical decision underlying this as well. While artillery at the time was not as destructive as one might think, military organisations in World War I certainly had access to some highly destructive devices. Mortars, for example, could throw explosive devices rather than the shells of guns and howitzers. However, mortars were surprisingly scarcely used early in the war, which has been attributed to their lacklustre performance in the late 19th Century before several advances in artillery design (Marble). So then why not, as you say, annihilate the enemy position by any means possible? This misses the point that the objective was to gain territory, not destroy the enemy. By destroying enemy defensive positions completely and laying waste to the territory, a military force would simply rob itself of any defensible position for themselves to gain during an advance. Artillery was, however, used to fairly devastating effect in defensive emplacements where they could be much larger (naval, coastal, siege, etc.)

If you want more detail, King of Battle's section on artillery by Marble is quite detailed and has great terminology breakdowns for a non-expert.

So, why did the artillery ever stop, save for potential shortage of ammunition? Like, just absolutely annihilate the enemy's position, then their reinforcements, and so on?

Consider the bombardment at the start of the Battle of the Somme: 1.7 million shells fired by the British artillery in the 5 days preparatory bombardment and the 1st day of the battle. The British produced 37 million shells in 1916, so this was about 1/20 of the year's British shell production fired in 1/60 of the year over less than 1/4 of the British front. To maintain this weight of fire over the whole front, continuously, would have required British shell production to be 12 times higher.

Over the whole Battle of the Somme, just under 5 months, the British fired about 17 million shells. That's almost half of the year's production, fired in 0.4 of a year, over less than 1/4 of the front. To sustain this rate of fire would have required shell production to be about 3.5 times higher.

Neither the preparatory bombardment nor the ongoing artillery fire during the Battle of the Somme succeeded in annihilating the defenders. Shell consumption greatly exceeded production during the battle. Thus, it was not possible to win through shellfire alone.

It should also be noted that if the only perceived threat was shellfire, the frontline trenches would be only lightly manned, with the majority of the defenders in the front lines sheltered in deep bunkers. It is the threat of infantry attack that forced the enemy to commit so much manpower to the trenches - without that threat, there would have been fewer casualties due to artillery.

None of the above should be read as artillery being ineffective. It was very effective, inflicting perhaps 65-85% of casualties on the Western Front, and provided essential support for infantry attacks. Effective, but insufficient to bring victory on its own.