Parent with Alzheimer’s is not mobile. Why does he keep wanting to go to the bathroom, but not use it?

That can be any number of things. A UTI, enlarged prostate, constipation, OCD behavior from the Alzheimer's, boredom, agitation, anything. Your father may just not remember that he went to the bathroom only a little while ago.
Start with taking him to his doctor. If a physical reason is ruled out, then maybe the doctor will prescribe medications to help with an OCD behavior and agitation.

Is he having trouble voiding urine or defecating ? Does he have a history of prostate problems ? Has he been checked for a UTI ?
If these things are ruled out then it will be behavioral due to Alzheimer’s .

Has he been checked for a UTI? This can be one of the symptoms. Even after urinating, you can still feel the urge to go.

It could be a sign that he's developed some OCD behaviors as that is very common with dementia. The good news is that there are some medications to help with that. I would talk to his doctor and see what they recommend.
In the meantime, buy a bedside commode and put it right next to his bed or chair so he doesn't have to travel far.
Best wishes.

A doctor should determine if he can't go for psychological or physical reasons. It could be signs of a physical problem. My wife had something that got worse from not being found early.

It can be a symptom of a UTI that is present.

Just keep an eye on it.

When Alzheimer's is present, the brain isn't firing signals properly anymore so your father thinks he has to use the toilet when he doesn't have to. This can be problematic since you say he's not mobile. Dress him in Depends or similar incontinence briefs and encourage him to void in them rather than the toilet. As AD advances, you can wind up taking him
to the toilet 50x a day otherwise as they tend to become OCD with such matters!

Best of luck to you.