They're much easier to get in and out of a car trunk where you're lifting at odd angles and more pleasant to carry up stairs to an apartment or office where there's no elevator.

Speed increases on steep enough hills (where most of your power is going into overcoming gravity instead of aerodynamics) are inversely proportional to total weight.

With 75kg of rider only, loosing 5kg going from a heavy old bike to a 9kg (entry level) contemporary road bike will make you up to 6% faster on the steepest grades. Making some assumptions about aerodynamics at 250 Watts you'd gain 5% going from 15.2 km/h to 15.9 km/h on a 6% grade. Dropping another 2.2kg to the 6.8kg minimum allowed for UCI sanctioned races would increase the gain to 2% from an average road bike or 8% from the heavy setup on steep enough grades or boost speed to 16.3 kilometers/hour on a 6% grade which is a 2% gain from the normal weight bike and 7% from the heavy one.

On flat ground dropping the full 7kg of bike weight might increase your speed 0.4% from 37.66 km/h to 37.84 at 250W.

Such differences aren't significant in terms of performance (cyclists have a hard time gauging effort within 10%) if you're not an otherwise competitive cyclist racing up a hill where it may make a difference in your placing.

Feel can be really different though - 6.8kg of pannier and luggage is very noticeable out of the saddle for me.