Inventory is the current asset most likely to be worth less than its carrying value when cash is urgently needed, so removing it gives a harsher and often more honest picture of near-term solvency.
For a business with a fast days-inventory-outstanding, the gap between current and quick ratio is small and the distinction hardly matters. For one holding six months of stock, the gap is the entire story.
Example: Northwind Tools has $570M of current assets less $265M of inventory, so $305M against $310M of current liabilities: a quick ratio of 0.98, materially tighter than the 1.8 current ratio.
Related: current-ratio, cash-ratio, inventory, accounts-receivable, days-inventory-outstanding