Because Sovereign makes it very clear that each Reaper is an Island unto it self. If they can't beat the Reapers in conventional War why do you think going after the Guiding Intelligence would help? Best case scenario when it is under attack it summons every Reaper to defend it. Resulting in a conventional War that they would lose. Crucible goes after the intelligence's tools. Effectively rendering it unable to fight back for the time.
At the time we spoke to Sovereign we didn't know about the guiding intelligence at all. They don't know exactly what Sovereign meant. We also know that he was exaggerating when he talked of having no beginning, so why might he not be exaggerating or misleading with that statement?
The fact that they can't beat the Reapers in a conventional war is exactly why they should go after whatever is controlling or leading them. It might be their only chance for all they know. Why put all their eggs in the Crucible basket considering they don't know what it is or what it does and don't have a necessary piece?
Or again less a priority because they have to deal with Reapers first. Or lets put this another way if you are playing a game lets say Dark Souls and one boss is currently beating you without you dealing any damage to them over and over again. You do not focus on the final boss. You focus on the boss currently curb stomping you into oblivion.
Or if your in WW2 during D Day you don't worry about Hitler's house you worry about the Tanks and fortified machine gunner nests facing you as you attempt to land on the Beach. Then only after those have been taken care of and a forward base of operation has been established and fortified so you can continue to land troops and supplies from a waiting boats without worry about the entire operation being destroyed by a few well aimed artillery strikes. Then you worry about Berlin.
If I'm getting beaten by that boss so badly, but could leave and beat the final boss, therefore not needing to fight the boss that's beating me, then sure I would.
D-Day was just one operation and cost thousands of lives. If they could have taken out Hitler's house and made the D-Day invasions unnecessary, then sure they would have. It wasn't that the beaches were a more pressing concern, it's that taking them was necessary to strike the interior of Europe.
As of Leviathan, the Alliance is shown to be using resources for things other than shooting the Reapers with guns or building the Crucible.