Is Infinite City Spam a good strategy on Immortal/Deity in Brave New World?

This comes down to the meaning of "Viable", so in this case, I am going to define viable as "Is this a good strategy on a typical Immortal or Diety game"?

ICS is not a good strategy on Immortal/Diety. You described several factors contributing to the decline of ICS, but most of them are managable. Happiness can be dealt with relatively easily using a combination of religious buildings, circuses, the liberty policy granting +1 happiness from city connections, and normal city buildings to spam an arbitrary number of happy-neutral cities fairly early on, so long as you limit their size when needed. So ICS is possible. However, its not viable.

However, while ICS is possible, its not a good strategy. One thing has shut down ICS, The fact that the incremental value of cities beyond the 4th has been decreased over and over again, until it becomes a dubious proposition to keep any city without excellent positioning or wonders.

This decrease in value has come in at least three separate places. The first is the science penalty per city, which is a very serious problem. On harder difficulties you spend most of the game behind on science anyway, so you don't want to take even more penalties. The second is the significant decrease in power for cities that don't have good resources. Resources are more important to making a city worthwhile than they were in civ 4, and the removal of bonus gold from river tiles has compounded that in BNW's new economy. The third is the tradition tree which is a very strong strategy that rewards you for the 4 city start.

The removal of whipping is probably a separate issue that also hurt ICS relative to Civ4 by ensuring that you have to halt production on something to build settlers, instead of "paying" hammers and gold over time (in the form of lost income)

Apparently this depends on map size and who you are play against. ICS is not a popular strategy on standard or smaller maps (for good reasons), but is almost an imperative for huge map. Because the AI gets huge bonuses on higher difficulties, especially happiness bonuses on King and above, they tend to expand aggressively if left unchecked (this can be really terrifying combined with their advantages in terms of production, science, and policy costs). The only way to (hopefully) offset this is to have as many cities as possible yourself. Having many cities equals a large science output/GNP (the increase in science cost per city is reduced on larger maps, which also renders ICS viable). It also equals more diverse luxury resources, and more strategic resources. Having cities on strategic positions is also going to be a big advantage in later-game wars, especially when air forces are in play. The AIs are really good at continuous expansion in later-games. So should you be.

The only real challenge for ICS is unhappiness. Luckily, I think BNW actually provides many great ways to reduce unhappiness. There are two first-tier ideology tenets for each ideology that promote local happiness. More is to follow in the second tier. Therefore, a large empire with 10+ cities can get 50+ happiness through ideology adoption alone.

To spam more cities without suffering unhappiness, you definitely need to consider getting some happiness related world wonders (e.g., Notre Dame, Chitchen Itza, Forbidden Palace, and Taj Mahal). Even if you don't want to expand too early, getting Notre Dame should still be a priority, not only because of the useful +10 happiness and +4 faith, but also because the AIs getting this wonder tend to expand very aggressively in the late medieval and early renaissance era, so rushing for physics and preventing them from getting this is probably a good idea. The Forbidden Palace is also a good one to have. The -10% unhappiness might not amount to much if you only have 3 or 4 cities, but it is a big deal when you grow to 10+ cities. Do note that the Forbidden Palace needs patronage. Given that patronage is not a popular policy tree, some would consider this a waste of policy point. However, this should also reduce competition in terms of wonder-building.

I would also consider the liberty social policy tree a must for a "wide" empire. On standard maps, people going for higher difficulties will usually favor tradition over liberty, since 60% of the time you will be holding on to 4 or less cities anyway. But this changes with larger maps. The +1 happiness from city connections (even with a city of population 1) is quite useful in offsetting the cost of expansion. Apart from the liberty tree, you can still devote 1 or 2 points to tradition and other trees. Grab the traditional opener for a handsome amount of early culture and Aristocracy to further boost happiness and wonder-building, for example.

If you manage to do well on all of these, then I guarantee that you will find ICS not only viable but also quite useful on larger maps. Sometimes, a wide empire with dozens of cities can actually end up with higher happiness than a tall one with only a few cities (with the help of ideology and other social policies).

Respectfully, I'd disagree here. From my experience ICS works well enough on Immortal and especially on archipelago, even on Deity. At least with civs who can found a fast religion or mostly any civ on archipelago.

First off, although there is a culture penalty, the culture bonus from religious buildings in cities is huge - with just monument, two buildings and liberty policy, you get +7 culture from every city. This is a bonus up till 140 culture production in your capital on a huge map - meaning early on it is monstrous.

Second - is the tradition opener really so cool? Yes, the first policy is much better than liberty's in the beginning. But then you have to place two policies which do virtually nothing, while liberty gets a production boost and a free settler. I'd say that at least there liberty is hugely faster than tradition.

As for hapiness, with two religious buildings, placing on a lux and city connection - any city can support 5 citizens without any hapiness building. On archipelago, this can be another +3 pretty soon from naval tradition.

With church property, market and at least 1-2 gold producing tiles, each city easily covers itself in gold, giving extra production for military units, culture and tourism.

The only problem is science, in which you will likely lag behind compared to pure tradition civ BUT on archi this is easily negated by getting cities with fish, which are plentiful. On a huge map the penalty is 2%, which means your capital would have to have 50 times the output of your next city for it to be negative. Even with cities of 5 people, this is unlikely.

On archi, new cities get a huge production boost. Combine this with order and the late game improvements and each city is a huge boon almost no matter to where it is located.

TLDR - on standard map, with say Denmark, Deity, no sea and no possibility od starting religion ICS sucks hard. However as it gets more sea, more religion and bigger map, I'd say ICS is MUCH stronger than purely wide empire. That is at least going for military or culture. I'd say on par in science and a little slower in diplo.