Magic are a major part of fantasy RPGs especially in the various editions of D&D. However it's impact on the setting is highly subjective and dependent on the rules that govern magic for a particular system.
For GURPS, the system I have the most experience with, my opinion that raw GURPSwould result in settings that would be a lot like ours but 20% better. People would be healthier, and wealthier, but it would not result in a societal revolution at the medieval level of technology. This is many because to do the really earth shattering stuff in GURPS you need to have a good number of points. To get that number of points on a normal basis would require a lot of hours of study. During which time you need to be supported with food, water, and quarters. At lower levels you may be highly effective in combat or in crafting but it cost an order of magnitude less resources to get the equivalent capability by having a larger quantity of people doing it a mundane way.
However in many situations magic will make a different hence the +20%. Plaques will be less deadly, harvests more reliable, life expectancy a little longer. Make magic easier to learn or more power quickly then technology level where a magical revolution occurs will drops. Like our own industrial revolution all the rules of society and economics will changes after a magical revolution.
So that is GURPS what about D&D more specifically the form represented by Swords & Wizardry.
The bottleneck is that vancian spell system. You got a slot you can cast a memorized spells from it 1/day. This can be modified by how easy it is to create magic items especially potions and scrolls. Last outside of adventurers (i.e. the PCs) how do people advance in magical ability (or levels). How long it takes?
One thing is clear that like GURPS S&W/OD&D you need to memorize spells. That is do nothing else for a set time in order to have a spell memorize and ready to do. That time not spent farming, herding, or otherwise working. Luckily in our own history we have analogous situations and the medieval monasteries, universities, and cathedrals. Earlier still we have institutions like the Library at Alexandria or the Academy at Athens.
From this we know that if magic doesn't help food production that it's practitioners are going be very limited in numbers. At lower levels of technology the surplus food to support people doing nothing but studying is limited. Plus it will be competing against things like the needs of the nobles, the craftsmen, and especially those of religion.
The more magic effect food production the more surplus there is to support extra stuff. Note it may not just need to effect yield, achieving a more consistent harvest would also have a similar effect.
Let's see what the Swords & Wizardry Core Rules has.
Create Water is a 4th level spell castable by 6th level Priest. A fair amount of training is going to be needed to cast this spells. And it is limited to water for 24 men for a day. Although starts doubling at 9th level and after. Create Food is the same way except it is a 5th level and needs a 7th cleric to cast.
My assessment of this is that cleric dominated groups can easily support themselves. Even a small temple in the middle of nowhere with a 9th level priest in charge can support 48 people with food and water. Lower level staffer can supplant the head's guy's casting allowing a surplus to be built up. These spells are limited to clerics as well. Suggesting that in society clerics have a serious edge over every other profession either adventuring class or mundane.
Control Weather can both increase crop production and harvest consistency. It is a 7th level spell and it's limits are at the referee's discretion. Unfortunately because it is a 7th level that means a 17th level Cleric going to need to cast it. However on the Magic User side it is a 6th level spell which means you only need to be 12th level to cast it.
This suggests to me that the heart of a religion where the pontiff, patriarch, etc resides are regions would have blessing of that religion and experience very regular harvests and the highest yields the technology allows. More common; areas dominated by Wizard Towers would experience the same benefit.
What all of this leads to me to conclude that a world with S&W's vancian magic would one where clerical organization have a qualitative advantage in being able to support themselves. This allowed clerics to gain an edge in any activity not involved in food production.
In western Europe's history the monasteries first developed as self contained communities to allow the monks to get away form the world in their pursuit of understanding God. From Fall of Rome to the 8th century everybody in Europe was fighting to survive in the Dark Age in the ruins of a once empire spanning economy. Alone the monks had the resources to be literate and pursue an education. So soon after they shut themselves in the world came to them to come back up and help them patch things back up. For many centuries the minutiae of trading, and administration was handled by monks.
With the clerics the use of magic make this impact even more out sized.
Likely at the dawn of civilization, society is dominated by theocracies and the rules are priest-kings. But due to barbarian invasions, chance, and time, the overwhelming dominance of the theocracies are challenged by republics and kingdoms. The efforts of the two are bolstered by the magic-users. Since all-important Control Weather can done with less experience by the magic-user, the kings and councils of the different realms can reasonably find themselves with one or more wizards capable of doing this. Also Magic User are somewhat more controllable with the vulnerability of their spell book. Take away and then the spells are gone forever after being casted.
There are a lot of dials here you can play with and the results is that many types of settings can result even they all share the same assumptions I am making. But by doing this type of exercise you find yourself considering the different possibilities. This is can ultimately to a more interesting and fun game for you and your players.