Look, unless you are roleplaying something, Agrarianism is never, ever, ever better.
I disagree
This is a game about the industrial age, not about farming.
The game is about growing you're economy and making money. In particular it's also about "you, the state" making money.
So the thing with farms is that they have 1/3rd of the construction cost of a factory and since a factory often takes the equivalent of a farm or mine to fed it with input early game 1 factory + feeder is about equivalent to 4 farms in construction cost/time. This means that for the same construction cost:
1) the farms employ more people that are going to pay tax, about 20K vs 10K
2) the farms output more units of a good, when tariffs/consumption taxes apply to that good the resulting tarrifs/consumption taxes are higher, considerably higher when it's for example opium
3) the farms at nominal price generate a higher revenue
Further considerations are:
4) you don't need to build any support industry, or can highly minimalise the amount
5) farms use up less infrastructure
6) a almost pure farms oriented build early game can allow for better tech focus
7) you don't have to stay Agrarianism all game, it can be more interesting early game and witch later going into -> 8
8) with mutual funds you can switch ownership of the farms to capitalists
Lets start with point 3 and 5. Typically before the 3rd/last production method of factory's farms output a volume of goods that at their base price generate more revenue for the amount of construction points invested than building factory's and it's supporting industry does. It's fairly significant, about 30 to 50% more revenue depending on the case. So building farms all prices being nominal will result in faster gdp growth, and before railways you can stack more revenue generation in a province with it's limited infrastructure than with factory's or alternatively farms will tend to require less infrastructure investment going further. You can check it for every factory/mine, i have done so myself, only things like sulpher, gold and oil tend to generate more revenue per construction point invested at nominal prices than farms. Not all farms/plantations being equal opium certainly stands out as generating a lot of revenue after upgraded to automated irrigation.
Note: i'm saying nominal price, however the above is even a stronger consideration when certain farm goods can be sold at very high prices, which is true for some under some circumstances from the early game on notably a number of high pop opium producing country's in Asia but plenty of others aswell.
About point 1 and 2. Lets consider how much the state is making specifically for each construction point invested. There are several ways to make money from what you build, this can be:
A) money made from taxes, as people work there earn money and pay taxes
B) money made from consumption tax ,if you expand production of a good that can fill more demand and you levy consumption tax on it then producing more units will yield more consumption tax of the bat
C) Money made from tariffs: if you expand production of a good you export so to increase the trade volume and you collect tariffs on the trade you will earn more tariff income from expanding it
D) the investment pool: If you're expanding relevant production the investment pool will add funds for it
Now the thing with all these points is that "you can have it all", but that point can also motivate you early on to build farms and nothing practically nothing but farms. Some country's just start out with big potential trade partners nearby that have a big demand for certain agricultural goods where you are better positioned to fill that demand. So if i'm for example Spain and i start out by building large tobacco and coffee plantations for the french market it will allow me to increase tax income faster, i will also get rising consumption taxes on those goods for each farm build and increasing tariff income for these goods for each unit sold across the border and my farms will produce larger amounts early on than factory's could of comparable goods.
But what regards for D, the point could be made that you could still do all this in interventionism. Well, if you're going to build farms pretty much exclusively for the first 2 decades or so then you're really quickly adding to the aristocrats investment pool and drawing from it, and because the farms generate more revenue per construction cost what the aristocrats collect is pretty large however the effect is stronger when a country can sell a lot of it's agricultural produce at high prices.
For what regard point 7 and 8, at some point you will want to build factory's and the notable reason why factory's are truly interesting versus farms is because at higher production methods they can yield more productivity per worker than farms, the caveat being that factory's arguably only really become interesting once a country has already employed almost all its former subsistence peasants. At this stage it would be interesting to change part ownership of farms to capitalists and to go laissez-faire, as well the farms only give part of the profit to capitalists by virtue of it being a sector generating a lot of revenue early on its contribution to the capitalist investment pool would be significant too.
Lastly point 4 and 6. There are points where such a strategy can be further bolstered by more narrow tech aims and more narrowed down construction requirements. In the early game of a pretty pure agriculture focus you would want to avoid building any factory's when can and when expanding farms/plantations remain a more profitable option. Purely wood based construction sectors can be a good thing in this strategy for not forcing you to put time in iron and coal mines before the follow up to atmospheric engines is unlocked, especially if you can import a lot of cheap wood from Russia or China it can be pretty good. Like as Vietnam for example my early construction is all opium/coffee plantations and construction sectors without putting effort in wood or iron/coal production as i can build a lot of opium plantations in the time i would need to build those and those opium plantations allow me to very quickly afford me more construction sectors. Improved agriculture might become an early tech focus but more important first is railroads and the supporting tools, iron, coal, steel and engines to support railways which is a relative small deviation of further producing farms early on. After that you will want to get good tech for your iron and coal mines and improve the construction sector. A few more techs are useful on the way but pump jacks become a important goal for tech rush. I usually also use the fast accumulation of early revenue in this strat to build a bunch of university's as it's useful for country's for which this style fits so tech focus becomes cheaper to do too. By the time i hit pump jacks i suddenly have to build a lot of engine factory's but the rewards are great too as the relative sudden switch of a highly agrarian economy to it is very significant to GDP. And yet all before this time i havn't build a single consumer factory yet, no clothes, furniture, no luxury goods and preferably i'm rather importing glass and paper at this point than having my own factory's.
It's also because it also fits some country's like a glove for their difficulty's early on. a lot of these population rich country's for which this strat works well have a big tax collection deficit early game which forces the consideration on wether you should start with building goverment administration buildings, however the return of doing so is higher once that country does not suffer any malus from traditionalism or hereditary bureaucrats while things like tariffs income is afaik not impacted by lower tax collection ability so that farming can generate more state income faster than building time consuming government administrations.
