How broadly a teapot matches with similar teas is entirely up to the drinker and their experience. For me, I use the same pot for all unroasted gao shan, whether it's Da Yu Ling, Li SHan, Ali Shan, etc. Others may be able to pick up on such subtle differences of seasoning left over in the pot that it might bother them and the notes could seem muddled up. Or, if those type of teas were my favorite and I drank them all the time, I'd probably pick up on the muddling and want different pots for each too. Ultimately, I'd much prefer one excellent pot to handle all gao shan, than 4-5 mediocre pots to dedicate to each type.
As far as the "reproducible result," I'm not quite sure what you mean. Are you asking if an individual pot works well for one traditionally fired TGY, will it work for all traditional TGY? Or, are you asking if one thin walled zhuni shui ping works well for dan cong, will all thin walled zhuni shui pings work well for dan cong? In either case, I'd say "not necessarily." Unless we are talking identical pots from the same batch, each teapot is a unique individual and will choose its own tea. Also every tea from different producers are unique too.
Having said that, I don't think there is always necessarily only one tea that will shine in a pot. Some pots are just made from excellent clay and fired well and can handle a wide range of teas very well.
Re: Yixing pot qualities for tea type
Thank you for sharing your experience with tea and teapot matching.
The answer to my first rhetorical question had been answered by teaism.
As everything in tea drinking culture is relative, this tea-teapot matching is also no exception.
I think this relativeness creates fun.
Because of this relativeness, we're sometimes like "fishing in muddy water".
As the end consumer, here we are the fishes.
As neither the fish nor the fisherman can see each other clearly, sometimes we (fish) lost the direction and just follow the artificial current created by the fisherman.
So we need to check regularly whether we're on the right track or we might end up being a donkey chasing a carrot on a stick.
In this case, what lost isn't only time and energy, but also financial resources.
The answer to my first rhetorical question had been answered by teaism.
As everything in tea drinking culture is relative, this tea-teapot matching is also no exception.
I think this relativeness creates fun.
Because of this relativeness, we're sometimes like "fishing in muddy water".
As the end consumer, here we are the fishes.
As neither the fish nor the fisherman can see each other clearly, sometimes we (fish) lost the direction and just follow the artificial current created by the fisherman.
So we need to check regularly whether we're on the right track or we might end up being a donkey chasing a carrot on a stick.
In this case, what lost isn't only time and energy, but also financial resources.
Re: Yixing pot qualities for tea type
This takes a lot of time, Betta. No getting away from the drinker. It's a point I've always found useful in balancing my own thinking. The drinker will always complicate things and try to put together an image from his/her own thoughts. But, all our thoughts our subjective, so let's have some fun and leave room for the thoughts of others. 
Re: Yixing pot qualities for tea type
Some of the best advice I've read on this subject was to just buy quality clay yixing pots. If it's a high quality clay, you'll be able to use it with some kind of tea. If it's poor quality clay, it won't be useable or valuable.
I can't find the post at the moment (would like to give the author some credit), but I've really tried to take this approach when searching for and purchasing pots.
I can't find the post at the moment (would like to give the author some credit), but I've really tried to take this approach when searching for and purchasing pots.
Re: Yixing pot qualities for tea type
This also takes some time and study to understand what is a quality clay. Ultimately, you have to handle older pots to see and feel what an older clay is like. If you're not in a position to constantly study this, you are disadvantaged dramatically when it comes to making a decision to purchase something. Then, you have to rely on someone else to help you.