There's been a fair amount written about what makes Stardew Valley so insanely addictive, but there's one reason that stands out above all others for me.
Because one day is always just a little shorter than I'd like it to be, I always have something I want to do the next day. Every time I go to bed I think "tomorrow's going to be great, because I'll be able to get this done", and in the morning, the feeling returns as "all right! Time to go do that thing!"
This has two major effects. Mechanically, it makes the game hard to put down, because this excitement happens right around the save point. Instead of the save being at a point where one can say "okay, I'm done for now", it's often right in the middle of a multi-day project. The emotional hit is, potentially, much harder, because if the player themselves does not experience this kind of excitement in reality, Stardew Valley is an especially potent surrogate.
Ideally, we would all feel this way about our real lives. Ideally we'd all be able to go to work in the morning excited for what we plan to get done or might discover. If the opening cutscene, where the protaginist decides to head out to the country because they're working in a cube for soulless Joja Corp., really speaks to you, there's a good chance the rest of the game will grab you pretty tightly.
Now that that's out of the way, I'd like to compare it a bit to another farm-based game I used to enjoy: SimFarm.
SimFarm was all the rage in my 5th grade classroom. Its approach to farming-simulation was much more realistic, but impersonal. There were no NPCs to interact with at all; all purchases were made through abstract menus. Crops were planted as standard-sized fields that required tractors with various attachments for upkeep and harvesting. The crops themselves were handled in a much more realistic fashion; they periodically had to be sprayed for pests or to prevent disease. Though there were no restrictions on when any crop could be planted, the harvest would be worthless if the proper weather conditions hadn't been met while it was growing.
This last point was rather maddening because fields would automatically re-plant as soon as they were harvested, regardless of the time of year. One could schedule this, but the scheduling window was rather arcane and couldn't be set to repeat each year, making it very tedious.
Stardew Valley gets around this last issue in a couple ways. First, it enforces seasonal limits, so that plants won't grow at all in the wrong season. All seeds are purchased and planted by hand, so there are no default settings to fight against, and the proper seeds for the season are always readily available and will always grow well. There's no consideration of how the local climate might limit one's choices within the available array of crops. It's a much more abstracted and simplified system, but the key is, it's more fun that way. The rewards of the system are more than sufficient to justify the number of clicks needed to make it work.
SimFarm often consisted of taking some time to set things up and then running through large parts of the year with the speed turned up, just so that time would pass until enough money was accumulated to do something else. Stardew Valley avoids this by providing all those other things to do--mining, fishing, socializing--to fill those profit and time gaps.
Though one could certainly make some visually impressive farms in SimFarm, it was often expensive to do so, when one factored in the large amount of land required by fields--and thus the relatively inflexible layout possibilities--the high cost of expanding the farm's area, and other expenses. So again, the game's bent toward realism acted against its potential for distilled entertainment and artistic value.
I think there's still room in the industry for a more realistic game like SimFarm, if it were given some layers of polish. Even so, it would have to run heavily on nostalgia, like Sonic does now. I predict junkyards of crashed crop dusters like the ones that once littered our 5th grade fields.