That's to simple! The food management is one part of the tactical range and depth of this and the tactical possibilities are the reason why we love this game.  If you cancel those parts of strategy possibilities  you don't have to play a strategy game like this. A mobile app would than enough! 

Abandon tiles on the planet for food. Pay a fee to increase farming output without graphical representation on the planet's surface.

Ok, as someone else said, even in todays tech we can pretty much grow food anywhere.

A planets base population should be based on it's class, this is a logical factor. Things like type of planet may alter this base.

So...

1. Every tile produces a base minimal amount of food, 
   1. larger class planets will then generate more food.
   2. this gives a base population based on planet class.
      1. which makes sense a larger planet will naturally support more life than a smaller one.
2. Most every improvement can POSSIBLY add to food improvements. 
   1. raising a specific tile food contribution.
   2. eco friendly buildings give more bonus, while things like factories give less (if any at all).
      1. Moral increasing buildings should give more bonus than other types (exception farms).
3. Farms (and other food producing improvements) increase greatly compared to others.
   1. They also increase food production on tiles around them.

This would allow those who want to focus on a food planet to be able to increase easily, while AI will naturally increase things by just placing improvements.

Non-carbon based life forms would get more food/pop from things like factories.

Planet types may also give base bonuses to tiles, so a water planet would likely produce more food than a dersert planet.

Easy math example:

If we take an average planet class/size of 8 and say it's base population is 4. Then each tile basically gives .5 food. I can place a farm which then either adds to (or even multiplies) the amount of food, thus increasing the population. I then build a park (moral increase), which has gardens and such and that may give a .6 food per tile. I add a factory and that give 0.0 food(for carbon based life). I then improve the factory which gives the tile another -.1 food (bigger more polution, etc). So when I'm done improving a factory, the base tile may be not producing any food bonus.

Okay, so if you're wanting a Food System that both AI and Humans can use equally well, then it seems to me that Food needs to be 100% predictable ie an If Population = X Than Food Production = X * 1 type thing. Remove the basic level of "must make food or my people will starve". Your folks will not starve to death if you don't build Farms. But if you do choose to build Farms, you make more Food for less money. So your population growth remains the same but your Treasury goes down by a smaller amount. Any excess food you get from your Farms becomes a resource that you can either Keep as a guard for Droughts, Disease etc (I'm sure there's a few Mega Events/random events that talk about Droughts and Disease but they could be improved to have a direct impact on Population, Morale and Food Production) or Sell it to another civilization/the Galactic Market.

So I'm wondering what size map and planet density everyone plays at and your opinion on food systems.

Cuz for me I try to play with fewer planets available so I won't have to manage too many colonies. Ideally like ten. Now I'm fine with the food system, but others have found it tedious. I suspect the difference might be because with fewer planets they can all be important and I still need to make decisions on where farms should be, while someone with more planets likely either has a planet with a food bonus, or planets with so little value they can cover several in farms and forget about them.

So am I right about this?

Anyone else concerned that we are this far in the game and seriously discussing changing one of the fundamentals of gameplay?

This feels like a GCIV discussion, not an "update" to GC3

I've personally not had any real issues with the food system as it stands.  I like to play Aquatic a good portion of the time, and the long road to awesome farms is a nice part of the challenge.

On the other hand, if there are to be limited tiles which produce food from the start, and only these can become farms, it seems that food will become a lot more strategic, and that is not a bad thing.

(indeed I am fellow aquatic, my favorite race is aquatic slavers, so first contact is often delicious)

Regardless, I trust Frogboy to make any new mechanics both fun and strategic.  If it were not Frog and Stardock, I'd maybe be worried.  I'm prepared to wait for several patches until it is balanced correctly.

cranial-rectal inversion.

Will this be a new invasion technique, frogboy?

The "food ship" thing was my idea but, of course, there's simpler ways of achieving the same thing. Be interesting to see if any if our blockade/starve the enemy ideas end up being used.

I was actually surprised to find the Version 3.0 Beta actually fairly enjoyable to play (of course I did "Mod" out a few things on the fly that I wanted changed) but the game has come a long ways since Crusade !!!  I have already gone ahead and pre-ordered the Intrigue DLC.

Revisiting my version 3.0 Beta play through today (while some Mods get updated for the Stellaris version 2.02 Beta Update 2), I still have concerns for morale on high population planets with cities but I don't see as much for the 25% population bonus per neighing adjacent Population Bonus Point from adjacent building  (Hospitals or Farms).  I still concerned for ability to get to high morale levels with needing multiple Morale Buildings and techs (supportive population +1 and Easy to Please +4) plus other factors (Celebrities and Race Traits).  Personally I might "MOD" back in recreation starbase modules although there never enough Citizens to have starbases associated with many planets on large and above galaxies.

Since Arable land is just randomly placed farms on the useable tiles on a planet and without regard to planet type, as Horemvore mentions, I like to see the current assignment of arable land tweaked (I still like to place my farms manually but maybe others don't - it could be a galaxy generation option).  Maybe limiting how many, if any farms, you can have based on planet type.  Or designate certain tiles as suitable for farming but don't force you to build farms on them if you don't want.  But I found in my play through with all the tech bonuses I had far more food available than I need if I built Cities on almost every planet, which I hadn't gotten to yet.  Every planet doesn't need enough food to have a City.  It might be interesting to split cities into Settlement/Town/City/Metroplex progression series to limit food useage and hence population (also addresses morale problem with high population planets)

It may need some modifying but https://www.nexusmods.com/galacticcivilizations3/mods/113 should do the job.