I thought monastery culture bonuses remain even after they become obsolete. Sistine artists are 9 base culture, I think. So with biology, a farm can support an artist -- it's not as population efficient as a town but it's not horrible.
Honestly, if we're constantly bulldozing villages/towns, we're probably going to lose to the AI. That's a big part of the reason why I don't think there's a need for a rule on those tiles.
The Culture remains for Monasteries that were already built, but that's not the issue with learning Scientific Method. Even in a Cultural game, you only really ever have time to build more than 1 or 2 of those buildings per City (maybe 1 or 2 more in the capital and likely less than 2 elsewhere) if you stop research (and pour on the Cultural Slider) before learning Scientific Method. With 4 other players playing, you'll be lucky to get more than 2 or 3 Monasteries built in ANY City, beyond maybe the AP Religion's buildings, which would still only give you access to 1 set of Cathedrals. That fact implies that if you want to spread around Religions, you're going to have to spend your turnsets running Organized Religion instead of Pacifism, meaning "good luck trying to spawn Great Artists" or that you're going to only try for Great Artists and the odd 1 Cathedral per City, meaning "you can't win since most of the Great People won't be Great Artists."
If, somehow, everyone else messes up their VCs and its in the 2000 ADs, then Culture might have a chance... but then all it would take to sabotage that VC is for someone to "accidentally" pave over a couple of towns with our otherwise standing-around-doing-nothing Workers.
If there is a belief that we likely will never get to Villages or Towns, or that there will be very few of them, then there is no harm in putting the rule in place, right?
It would be roughly equivalent to a player being able to "unlearn" the knowledge of a tech for a Space game... invested turns can be wiped out very quickly. Other improvement types, however, could be back-and-forth replaced with Farms versus Workshops and in that case, the players with different uses for the improvements could just quickly undo what the last player did (since we are not allowed to delete our Workers). But, there's no way to undo the paving-over of a matured Cottage.
It would also be similar to gifting-away Cities to an AI for a Conquest game, and we went ahead and put a rule in place to prevent that possibility.
We're just putting in a minor rule in place to deal with that game dynamic (the fact that Cottages are investments and if a player choses to invest in them as their strategy, they won't be screwed over due to maliciousness).
Even in a Diplo game, where another player could maliciously declare war on the AIs to sour relations, there is always the "capitulate your war target and get your Vassal to vote for you" way to win, so even that form of maliciousness can be worked around.
In a Cultural game, though, you generally either invest in Great Artists or in Cottages, although you can also try for a later-game Sid's Culture VC. Good luck getting 10+ Great Artists in this game, and good luck getting a lot of Seafood Resources for Sid's, leaving matured Cottages as the possible solution... but who is going to invest in working Cottages if all of their investment can be undone at a moment's notice?
The Corn + 2 Ivory site is in 2nd ring of distance maintance iirc, thou i think the guide i'm remembering about city upkeep is from before warlords so that might be out of date 
They're good for nothing if you use other improvements well. I mean, build them if you want, but they kinda hurt my eyes so... Seriously, going shops here is quite a no-brainer as they give us that much flexibility for everyone to do what he fancies for his VC. Making villages/towns invincible is probably rather counterproductive as each cottage-disliking player probably just makes sure all are bulldozed first thing in the set so we are just wasting tons of worker turns 
