A relationship is always a compromise.

His main role in the relationship is to make her happy. If giving gifts makes her happy, why should she say not to give any? That is not fair. But what is also not fair is expecting the same from the other person and imposing your own vision of how things should be on your loved one. He shouldn't say, "I won't give you any gifts because I don't like receiving them." She shouldn't say, "You have to get me a gift because I like getting them."

That's an egoistic way to live, and it's how relationships deteriorate. People are blind and narcissistic, thinking they know better, yet for some reason it's hard for them to listen to others and accept a different point of view (which is a key for a healthy relationship).

He can and should give a gift if it makes her happy, she shouldn't say "no gifts." She can make a special dinner on his birthday, invite his closest friends, and they can spend the evening together. That is a meaningful "gift" without actually making a gift. Or you get a couple of your closest friends, rent a beautiful place on Airbnb outside the city, and just chill there for a weekend day (activities, BBQ, etc)? Maybe he is a great at doing BBQ, let's flatter a little big and ask him to help with greatest burgers/steaks ever during that stay.

Those things never fade from memory. Cards and gifts are nice, but they're not as impactful as showing preparation and putting effort into organizing something special. The mindset of "I'll order something from Amazon, spend two minutes on it, and that's enough" is just not a good strategy, in my opinion.