I've been overly concerned about my cat Ms. Thang. She has never drank out of her plain water supply. I couldn't figure out the issue and still haven't. However I can offer you solutions that may help.
I discovered that Ms. Thang only wanted her water OVER her dry food! So now what I do is I put fresh dry food in and then put in luke warm water over it. She dranks the water BEFORE the food soaks it in. I may have to repeat this process a few times and get left with lots of soggy food to toss out later in the day. She likes her food dry .
She was drinking out to the toilet but not regularly and not every place we lived. However, now she likes to drink out of the bathtub. With or without me in it! What I do now is I leave just enough water in the tub for her to drink from but not get her paws wet. This is where she will drink plain water.
My suggestion is to change up your typical water routine and be flexible. I never thought I would use a bathtub to give water to my cat but it works. You just have to work with your cat to see what oddball habit he/she may have and work with it.
Cats are finicky creatures. Sometimes we have to bow to them!