It's indeed possible, and you can easily find already existing OSS ChatGPT implementation that can serve as a base. I am more targeting no tech people or just the ones who don't want to bother building it / hosting it.
Just seriously curious, won't you buy it because looks like it was created in a weekend? So maybe not reliable?
I'm in a similar mood, but most of the indie maker's products are created this way and some end up scaling pretty well and turned in good investments, as they are usually cost-effective.
It's not about reliability, it's just that, for things this simple, I'm inclined to write the two Docker Compose lines to deploy this to my Harbormaster server than to pay for it.
I'm very much the minority, as I like to self-host, but it seems to me that an OSS solution would do the same thing,and equally reliably.
Then again, the value proposition in this is that it's hosted and you don't have to deal with OpenAI keys, so that's what users are paying for.