I'd say, ask the user for a path where to save them presets, done. No ?
Which makes complete sense, but the interesting part about that is - on Linux, how best to do that? You can't necessarily just use an 'OS provided' file selector - because, you don't know what desktop / window manager / distro the user is running, so it might be (at best) GTK2 / GTK3 / Gnome or Qt, or even something they've created themselves and it would be a pity to have a plug-in potentially carry all the GTK2, GTK3, Qt etc dependencies just to provide that one function.
Most (commercial) linux plug-ins will use an X11 based file bowser e.g. via a toolkit like JUCE to provide the best / simplest compatibility - but X11 doesn't provide any 'widgets' itself, so it means writing your own file selector 'from the ground up' (which we already do e.g. for the license selector, but would require significantly more functionality for preset management).
It would be nice to be cross-platform - but e.g. on Mac OS, its essentially mandatory to use the OS file selector, not least because it provides the user with a consistent interface, but also because it best handles permission issues etc in a consistent manner (your user may not have permission to save presets to their chosen location for example, which requires the OS to present a dialogue to negotiate that).
Also, depending upon whether the host application is sandboxed (typicaly if it has been installed from the Mac OS App store) the path you select may not actually be where you think it is (your 'home' folder may map to some user writable location within the host 'App' bundle - for example, depending upon what sandbox permissions the host application may have)
So there are issues which are complicated by the fact that a plug-in is often providing 'application like' functionality, from within another 'host' - over which it has very little control. It can of course be done, but it needs to work similarly in
any host on
any supported OS. Which brings us back to, the general direction in which this is going is that the host is expected to provide the preset management (as in VST3, Audio Unit etc).