Hydroponic aquariums, as you call them, are not bad per se, they are simply an aquarium in which plants have their roots immersed. It's not much different from having an aquarium with floating plants, and many people (including me) have plants in their aquariums that only have their roots in the water. In my particular case i have pothos growing out of my discus tank, and all along the windowsill, several times, as I bend the vines backwards when they reach across the window. One of the vines must be well over 4m by now.
They are excellent nutrient sinks, because they are not limited by the CO2 in the water (usually the limiting factor in aquariums) as they have access to the unlimited supply of CO2 in the air. My corys also love the jumble of roots in the water as a natural spawning mop. I've had several generations of corys in that community tank.
The thing to keep in mind though is where the focus is.
In an aquarium the focus is the submerged environment. Any emersed or emerging plants will be a biological and aesthetic bonus, but what counts is what's under the surface.
In a hydroponic garden the focus is what grows above the surface. What goes on at the level of the roots of the plants only counts to feed the plants.
By all means, if your mother likes plants do get her a hydroponic garden, but don't consider it as an aquarium.
P.S.
Of course there are such things as paludariums and ripariums where the focus is spread between above and below the water, but it's not something that is relevant here.