Software built on top of that can be whatever we want within those limits. Even most proprietary operating systems are relatively general purpose. On windows and Mac os, you can generally acquire a wide range of software capable of doing many things and can create your own with relative ease.
Smartphones get a little less general purpose, again above the level of the actual computer though. In the case of smartphones and consoles and such, the extra software thwarting the general purpose nature of the computer is buried a little deeper as firmware flashed onto rom chips.
Then with computer powered appliance type devices, the only software is whatever is flashed onto the rom chip buried inside there that you can't really touch without some hardware modding.
In the end, computers have never stopped being general purpose, and likely never will. It's just the software separating the user from the computer is getting deeper and deeper into hardware.
I realize there's good security and user friendliness arguments to be made for this kind of thing, but it's a worrying trend. It'll create almost a pseudo class system with the people who have real computers and can use them to make money and do things and the people who have toys that suck money from them and feed them consumer garbage.
This is why scientific and commercial mainframes still exist, and why a lot of computing is offloaded to cloud services, relegating the modern OS on a modern CPU to a client system.
There are also entirely classes of fairly conventional applications - A(G)I, true holographic displays, pseudo-real telepresence, real-time photo-realistic rendering (although that's starting to become possible), distributed non-localised filesystems, associative semantic storage of all kinds - that modern hardware is still too slow for.
And more speculative classes too.
In fact contemporary hardware is mostly quite slow and dumb. It's incredibly fast, small, and cheap compared to a mid-80s mainframe, but it's going to look very underpowered and crude fifty years from now.
On modern pc/server/mobile computers it's impossible, your root of trust there is manufacturer and their microcode/embedded security modules with separate operating system etc
I'm not talking about apple turning down fart apps, I'm talking about the basic ability to write and run your own code without asking apple permission.
The most "general purpose" software most people interact with is a browser.