What does expansion valve and dryer do in the A/C system

Any time an AC system is open to atmosphere dryer must be replaced. Dryer has only enough desiccant to remove moisture once in system. So that is why dryer is replaced. Expansion valve is replaced when debris from AC compressor is carried through system TXV opening pin size slight particle will clog ie. No AC. A competent tech will replace both.

Your mechanic is selling you cheap insurance to guarantee the system continues working properly. The expansion valve has a tiny adjustable port the refrigerant goes through. By being small, that refrigerant is under pressure on one side, and once it gets through it goes to low pressure, expands, and that makes it get real cold. Whenever you open the system, especially to replace a compressor, debris can get knocked loose that plugs that port. The result is no cooling, and you have to evacuate the system and start all over. That is not the mechanic's fault so you can be expected to pay for the second procedure and the additional repair. Your mechanic is trying to avoid that.

The receiver/drier contains a filter and a bag of desiccant to absorb up to about ten droplets of water. Your mechanic will start by pumping the system into a vacuum for a minimum of thirty minutes. That will make any water boil at seventy seven degrees. When professionals open the system, they will seal the openings immediately to prevent air from getting in. That air contains moisture in the form of humidity, and that causes two problems. Water mixes with refrigerant oil to become corrosive and that will eat away the evaporator and the condenser from inside. That results in the leaks do-it-yourselfers typically run into a few months after doing their own repairs. The immediate problem is when a droplet of water circulates around and goes through the port in the expansion valve, it gets so cold that it freezes and blocks further refrigerant flow. The system will stop cooling until that ice melts in as much as an hour, then it will work again until the next droplet of water comes around. When the system is fully charged, that water is almost always the cause of intermittent cooling.

Your mechanic will replace the receiver/drier, do any other needed repairs, then evacuate the system to boil the water out. Any remaining water will get trapped in the drier so it does not cause a problem. Every air conditioning specialist understands how the system works and will replace the drier if he has your best interest at heart and wants to do a quality job for you. If anyone told you that is not necessary, I would be looking for a different person to work on my car.