Zyra isn't short range. She has quite long spell ranges. Longer than Syndra's for sure. She can one-shot people pretty well too. If you're saying Syndra's range makes her not immobile, you have to give that same consideration to Zyra. Xerath's ult... well, it's not the focus of his kit. His power comes from other avenues. Also, what does "he barely needs to move" have to do with whether or not he's immobile? He has nothing to make him move. Mobility is the ability to move. Immobility is the lack of the ability to move. Xerath lacks any movement abilities. That makes him immobile.
Also, who says Zyra and Xerath are useless? Xerath still sees competitive play (more than Ziggs does) and Zyra has plenty of success at high-level play. She's even come back into being a successful mid laner, not just a support.
And anyway, that's irrelevant. Whether they are strong or weak and whether their kits are desired or useless isn't really something that matters to whether or not they are mobile or immobile. Immobility can help make something useless or useful, but something's usefulness is not used as a measure of whether or not they are mobile or immobile.
Immobility and viability are not the same thing. A champion doesn't have to be crippled and useless to be immobile. They just have to lack mobility.