Why do old batteries take the same amount of time to charge
Older lithium batteries actually take longer to charge because oxidation of the plates causes their internal resistance to increase, which increases internal voltage drop and reduces the time that maximum charge current can be applied for without exceeding the maximum charge voltage. 

Most lithium chargers are 'CVCC' (Constant Voltage Constant Current). They apply a fixed charging current until the battery gets up to full voltage (4.2V per cell in modern Li-ion batteries) then taper the current off to prevent the voltage from rising any higher. The charger cuts off when charging current has dropped to about 10%. 

With an older battery the higher resistance causes the CC phase to be shorter and the CV phase longer. To get a full charge may then require charging for longer at lower current. However if the charger still applies the same constant current and cuts off at the same 10% then the battery won't get a full charge. Thus you may get a similar charge time but reduced capacity. The increased resistance also reduces the battery's energy output when drawing high current, and shortens the time it takes to drop to low voltage cutoff under load - thus reducing its effective capacity even more.   

As the battery ages its internal resistance eventually goes so high that the CV phase also gets shorter, and voltage under load is severely affected. At this point it is practically worn out - even though you might still be able to get useful capacity by charging and discharging very slowly.