With an external cache/CDN it should work perfectly fine.
There are also some caching plugins for wordpress, but most of them still hit the database on every request.
So I assume it's because it's not statically build, but requires a DB connection all the time?
Yes, with the recent waves of AI scrapers I have noticed on my own WordPress websites that the DB seems to the weak point when under load. Cache plugins can help a lot with this.