I'd like to see this as well, but I *think* (says the player who knows nothing about coding
so take with large grain of salt) it would be harder to program than it seems. With the current game limitations on giving help, I don't see how it could be done without accounting for certain bldgs not being available for polish (examples: all culture bldgs have current polish; all builders have been boosted). That would require a player be able to 'rank' their choices, so for example if Builder is top preference but full, it would default to 2nd choice C and if all culture bldgs were polished, it would default to 3rd choice MH. I think that would be more complicated to do than for example selecting 'favorite' on the AW's, the only other selection system I can think of atm in the game.
IMO they'd also need to do something about the MH storage limit of 20 helps worth of coins from NH before they must be collected to earn more. Cities in active FS's and a decent neighborhood who select MH first can now easily reach that limit daily. If their schedule is not such they can collect frequently, they get no benefit from another player visiting and donating to their MH. Once the limit is reached, the MH remains available to polish but the receiving player forfeits the benefits until they collect the existing limit. The only thing that saves them from getting *nothing* right now is that so many players ignore the request of 'MH Only' (as well as others like 'NO COINS!', lol!) such that they're not getting all those donations from all visitors.
At the moment, culture buildings are ranked from highest culture to least culture. On the request to generate the NH window, the server replies with the highest value culture item that hasn't already been polished. If there are no buildings left to polish, then much like the Builder's Hut, the option to select it drops from the menu. If the building that was selected got polished before you manage to hit the button, the server replies with an error indicating that the building was already polished. If that happens, you currently have to exit out of the NH window, and reopen it to get the newly-grayed out button to become green so you can try again.
The thing that performs the selection would, ideally, be a separate function that could be called to retrieve a valid-at-the-time culture building for which you can then select to have polished (or an empty result to indicate that there's none left). Ideally. It's also equally likely that the piece of code responsible is buried somewhere deep in the guts and would prove excessively troublesome to extract and still work as intended. Code refactoring is, after all, a pain that nobody wants to deal with.
If the former, then it comes down to the willingness to implement it and modify the interface to make it so. Which may make the design team throw a hissy fit. If the latter, expect a swift rejection followed by many months before someone gets sufficiently wasted one night and decides to hammer out a piece of miracle code to do the job
"just because they can". And then attempt to convince the rest of the dev team that they've brought gold that
absolutely has to be added to the codebase stat or else everything will halt and catch fire do it do it doitdoitdoit shipitbeforeitbreaks.
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That being said, I also fully expect that in order to make that functionality work, the game would need to query the availability of all items in all target cities on the page being opened before the user interface could show something approaching usable. Coupled with the amount of time such a page would need to be opened for to get to all the things, I imagine that the last couple entries on the list might be outdated by someone else doing neighborly help at the same time, thus throw errors more than one would like to see (which would preferably be never).
Storing preferences would necessitate changes to the database structure, which is something often quoted back when teleporting evolving buildings weren't a thing, and is sometimes still quoted when people wonder why (at this point in time) we can't teleport Ancient Wonders. Those quotes can summarized to be: "No."
Also, I can't imagine this being any easier for people to use as-is for those who has problems or simply dislikes doing precision clicking to make a particular irrevocable transaction. The trader is bad enough; I wouldn't want the devs to inflict that on all of us here as well.
I also waited to put out this post until I could perform an actual NH request to examine what the server sends back. There's a lot of speculation, and I'd rather not be wrong on something that's easily verifiable. NH attempts do, indeed, reply back with available buildings (along with other funsies, like what sort of rewards you ought to get when you do give help), which implies that the selection is done server-side. Thank goodness for the forum's ability to autosave drafts of a post.