Dynamic loading of content is a feature of SPAs, but it's not a defining feature, nor unique. In fact, one defining feature of SPAs is the offline capabilities (service workers, caching, etc.), which sits at a bit of a tangent to database considerations like this.
Even in the most simple scenarios, you quickly find your limits. If you get data back, but it's paginated (and it almost always has to be, for basic reliability reasons as much as anything else), you can't be guaranteed to have the complete set of data in a given circumstance, so you can't perform operations like filtering, pivoting, or sorting that data locally. You have to ask the server to do this for you and wait for the response, just like we've had to in the past.