Among other issues, the ANV had artillery, too. The available positions for the Federal guns to have clear ground for firing (outside the town) would have been significantly exposed to counter-battery fire, as well as having crews and horses killed by small arms fire. The major problem with Burnside's attacks on the Union right was the killing field they had to cross, not the stone wall.
It would be a bit crowded pushing guns, caissons, etc. across and through the town along with troops and other vehicles. Then they'd have to find room for the artillery to set up behind the infantry, all under fire as @Belfoured said. The guns would be firing right over the heads of their own troops, and would probably have to cease fire when the assault went in.
A smashed stone wall is still a pile of stones, pretty good cover. Presumably the rebs would take cover while the bombardment was ongoing and resume their position when the Union infantry attacked.
Marye's Heights was about a mile from the Union guns on Stafford Heights, close to maximum range for rifled guns. I understand weapons like the 3" ordnance rifle were pretty accurate; would it be feasible to bombard from across the river? Some of the Union guns, where the river curved at the north end of the battlefield, were a bit closer, possibly in position to enfilade the Confederate lines. Maybe a role for the 20-pounders or other heavier weapons?
The fight on Marye's Heights was supposed to be a diversion with the main effort being made by William Franklin far to the left. Unfortunately, Franklin seriously dropped the ball and Burnside just wouldn't let up against the heights even when it was clear that Franklin's effort was a failure.
That said, there just wasn't a place for artillery to deploy that wasn't under the guns Longstreet's artillery to the front.