Can vs Could usage differences

But I learnt could is also used for hypothetical forms also. Why can’t we use “could” here in hypothetical sense or to show possibility?

Because when you said "he goes to London" you expressed it as a definite action, not a hypothetical.

You could say,

He goes to London every month, so he could see his father (if he wanted to).

(By removing the that we make seeing the father a hypothetical consequence of going to London, rather than the reason for going to London)

or,

If he took a day off work, he could go to London so that he could see his father.

(making going to London a hypothetical and thus seeing the father also becomes hypothetical)

Preterite forms are used for ulikely or impossible situations (modal remoteness) in conditional constructions, e.g.

If I went to London tomorrow, I would visit my ailing father.

The first of your sentences does not depend on an unlikely or impossible condition, but if we made it modally remote, it would read:

He would go to London every month, so that he could see his ailing father.

This gives the sense that this situation isn't true or likely because some condition remains unfulfilled. The condition could take two forms: one with irrealis were, or the other with a modally remote preterite form.

If he were able to (now or in the future)...

If he had the chance now (now or in the future)...

Both of these are referring to a hypothetical situation in the present or future and hence the preterite forms were and had do not mark past time but modal remoteness.

In these sorts of constructions, the verb in the outcome clause must be a modal auxiliary taking a modally remote preterite form unless there is none. (CaGEL p751)

Accordingly, the verb in your second example's main clause

He goes to London every month so that he could see his ailing father.

needs to be changed to meet these conditions.

If he were able, he would go to London every month so that he could see his ailing father.

Of course, we might also substitute other modals for would - should, could, might, etc.