Hello benzenering: Hm-m-m-m-m... well... I'll tell you I've seen a number of therapists for brief periods over the years. They ranged from mediocre to dreadful!

I don't see a therapist anymore.

For me it's simply not worth the time & expense. Plus, there are things in my background I simply could never talk about with anyone.

So there's a definite limit to how much even a great therapist could help me (assuming I could find one.)

I'm also an older person. (Even older than you!)

And personally I do think that, for a variety of reasons, therapy becomes less beneficial as one gets a bit older. There's so much water that has flowed under the bridge, as the saying goes.
You wrote that your pdoc has sent you to therapy for your drinking, thinking that it is caused by low self-esteem. But you like drinking. (By the way, I don't drink anymore.

I used to. But I gave it up when I went on antidepressants. I'm no longer on any med's at all. But I still don't drink simply because it costs money & I'm now on a fixed income. I've always loved the taste of most alcoholic beverages.) From my perspective, I think the question here is... are you drinking to the extent that it's damaging your health. If not, & if you like it, then I personally would feel as though going to therapy for it is pointless, unless you agree you are struggling with low self-esteem & want to try to get at the root of that problem.
The thing is you have to be invested in therapy for it to be of benefit. And therapy takes time & effort to work. If you're just going because someone else said you should, then (I believe) it's a waste of time & money. And as far as the 6 week time-frame goes, my personal opinion (again) is that it is really beside the point. There again, you're either invested in therapy or you're not. If you are, then there should be no arbitrary time limit. But if you're not then why get into it in the first place?
Now, of course, the other consideration that comes up here is whether or not the therapist you're seeing is someone you feel comfortable with & who you feel is helping you. If not then, at some point, you may want to consider looking for a different, more compatible, therapist. However, there again, I don't personally think one can set an arbitrary time line on that. It's simply a decision one arrives at over time.