How is the effect of wind on arrival time handled?
It will depend on constraints at the arrival airport. If there are no constraints, they will choose a speed that minimizes fuel burn, and arrive early if that's how it works out.

It's possible that the arrival airport may have constraints on arrival volume. As you pointed out, for busier areas, if aircraft arrive earlier than expected, it could cause things to get backed up. In that case ATC may have an aircraft adjust their speed or enter a hold in order to delay their arrival until capacity allows. Slowing down early is more efficient than arriving too soon and having to fly a holding pattern.

In areas without radar coverage, such as oceanic crossings, aircraft may be required to hold a certain airspeed in order to maintain separation from aircraft ahead and behind. In this case a pilot may not have much choice until they exit the oceanic airspace, and any adjustments would have to be made after that point.

ATC will do their best to ensure the safe and expeditious flow of traffic, but safety has to come first. While a pilot can choose to not follow ATC instructions in the case of an emergency, and in the interest of safety pilots have some amount of discretion in declaring emergencies as they see necessary, doing so just to reduce cost or for convenience would not be acceptable and may attract some scrutiny.

It's also possible that there would be constraints on the ground at the arrival airport. If the aircraft is scheduled to arrive at a certain gate at a certain time, and it arrives early, there may be another aircraft still occupying the gate, or support staff may not be ready to receive the aircraft. This would require the pilots to coordinate with the airline. If alternate arrangements can't be made, the airline might actually prefer the aircraft to be not arrive early. They would probably prefer to sit on the ground, with the engines off if possible, as that burns much less fuel than doing the waiting in the air.