My son has a 2002 Altima 2.5S. Occasionally the brake pedal has excessive travel. The dealer can’t replicate the problem, but my son has already had an accident because of the pedal travel. We’ve replaced all the brake pads.
Bad master cylinder.
I agree that this is a bad master cylinder. Since your experience does not say anything positive about that dealership, I would suggest that you go to a well-reputed independent mechanic to have the master cylinder replaced. And, even if the mechanic does not mention it, make sure that you specify that you want new brake fluid to be used when the brake system is refilled.