They absolutely can, if your workload is ideal for this situation, but unfortunately, the most "expensive" (in terms of time, money, computing power, you name it) part of giving a user information is typically the filtering and collation of that information from a much larger pool of information — almost always a pool of information that is far too big and too private to just send to the client to sort through locally.
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.
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.