Yep, I'd agree here. I think what needs to happen is multi-fold - more specialist spots, and more powerful specialist spots. Likely what it should be:
-Tier 1 building has 1 specialist spot. Tier 2 has 2, and Tier 3 has 3. So a city with a workshop/factory/PP can run 6 specialists in the industrial zone, to further simulate more people working in the city.
-Somewhere around industrialization, specialist yields double. This essentially brings them in line with tile improvements, as an industrial zone specialist would be 4 hammers, which is not much worse than a plains mine is at that point in the game
-We already have increased housing (Neighbourhoods) and increased farming output (Replaceable Parts/Mechanized Agriculture). What we're really missing is a modern way to increase your amenity count. I find myself when I get to the modern era, my population explodes and I basically have to go build entertainment complexes in every city to even have a chance to keep up. And while that's not necessarily bad, it feels like there needs to be some way other than rushing to Democracy and New Deal to get amenities in modern times.
I don't know what the proper solution is to that problem, whether it's a way for luxuries to stretch to more than 4 cities in later eras, or for factories to produce new luxuries, or simply a mechanism where specialists don't use up amenities or don't use them as fast, but there definitely needs to be some way to increase your amenity count late other than mass producing arenas.
The Industrialization/Industrial Revolution involved not only Factories, which as a concept dates back to the 18th century, but also the specific Technological advance of Steam Power applied to mass transit, railroads, and water (river AND sea) transport, and specific Financial Advance of Joint Stock Companies and Mass Stock Exchanges, which allowed the accumulation of massive amounts of capital to fund all the new technologies and changes.
The transportation changes changed not only intercity and inter-country/continental transportation and trade, but also intra-city transportation: even early 'commuter' steam railroads allowed cities to expand dramatically in size: central Boston between 1850 and 1887 extended from about a 1.5 mile radius to over 4 miles: that means the area covered almost tripled, and that kind of area increase was mild compared to Paris, London, or New York in the same period. That, in turn, reinforced the combination of More Jobs (Factories), More Food (railroad/steam ship transport), More Health (Sewers, Public Health facilities) to blast Urban populations through the roof in the late 19th century (late Industrial Era). No Single Change would have done it: you need all of them.
The game could simply apply changes by Rule: build a Factory, get X increase in Production, Population, Amenity, England automatically gets a Boost with Industrialization, etc. This is absolutely WRONG. If as Norway I have access to Coal and Gold and Education and already have international Trade Routes, why can't I get the Initial Industrialization/Factory Boost? IF I build factories but fail to build railroads and have little international Trade and investment, am I going to get a major Boost from Industrialization, or am I going to end up looking like Imperial Russia in 1914, lagging way behind western Europe in Gold, Production, and, especially, Amenities - leading to Revolution in 1905 (failed) and 1917 (succeeded, so in Game Terms I suppose Russia Lost...)
Instead, we need to give the changes, boosts and bonuses to the combinations: Steam Power with Factories lead to Railroads or Railroad Districts, which boost population growth in the city, which requires investment in new Amenity-creating in the cities (it is no accident that Central Park opened to the public in 1858, an Obvious Amenity-Producer tied to the urbanization/concentration of Population).
Which brings us to the Late Game Amenity Problem. Simply Stated, Civ Games STILL equate Happiness/Amenity with Natural Luxury Goods: Wine, Furs, Ivory, Cocoa, Spices. Note that of that list, two (furs, ivory) are Illegal or disparaged in many parts of the world today, while Cocoa, Wine and Spices are all dwarfed in significance by the manufactured products based on them: brandies and liqueurs, chocolate candies and drinks, Packaged Foods. The 'High Value' Amenities in the Modern Era and later are all Manufactured Goods, ranging from personal automobiles to personal electrical and electronic devices (starting with the personal telephone and record player and radio right up to the personal computer and cell/smart phone). Value-Added since the beginning of the 19th century has almost always meant Added By Manufacturing.
We could have Factories in General produce Amenities, or allow Specific Factories, like the Shipyards now, which are essentially ship-building Factories, and we wouldn't even need that much 'specialization':
Automobile Factory - available at Tech: Replaceable Parts, can be either built in an Industrial District or Upgraded from a regular Factory. Produces 1 Amenity in every city linked to the Factory by Railroad, rising to 2 Amenities at the start of the Modern Era - or whatever trigger at that time we want to use to show the advent of the Interstate/Autobahn roads that allow mass individual travel almost any distance within any country.
Electronics Factory (Japan will have to get a new UB!) - available at Tech: Plastics, similar Build Conditions as the Automobile Factory except that the Personal Electronics Amenity Good produces 2 Amenities per city linked by Railroad, Aerodrome or Harbor to the Factory, increasing to 3 Amenities at Tech: Telecommunications.
Automobile Factories also get a 50% Boost when building Tanks or Modern Armor (because about 75% of all the tanks built in WWII were built in converted car or truck plants like Detroit Arsenal in the USA or Kharkov Tractor Works in the USSR)
If it turns out to be necessary, a similar Boost could apply to an Electronics Factory building Mobile SAM, Rocket Artillery, or Missile Cruiser units, all of which are heavily dependent on electronic components.