Strange how vastly tastes differ. The military aspect of the Civ games is my favourite part, I tend to completely lost interest in and quit games if there's not enough war.
One of the great strengths of the game is that people with very differing desires in the game can still play it and enjoy it.
"Quick Fixes" for a lot of the Resource-related problems that bedevil the game now are:
1. Do away with the fixed definition of each resource as 'strategic' or 'luxury' or 'basic'. The definition should depend on how your Civ is using it At That Moment. Copper could be the primary component of Bronze (strategic and Production - tools), but it could also be used for jewelry (luxury) and later for Electrification (Industrial Luxury and Production?). Elephants are early strategic, also luxury, today just largely Zoo Animals. Resources should be dynamic in their definition, depending on technology available and social, civic and other factors.
2. Make Resources desirable for building units, but not mandatory - as
@Bonyduck Campersang said, they provide a bonus to building but aren't a requirement. I would add that at a point in the Industrial Age that changes, because the requirements go up by an order of magnitude and strategically the game starts to become a race for resources: oil, grain, iron, coal, etc.
3. Make organic (animal and plant) resources Moveable, with some effort. If you don't have, say, Horses or Elephants or Cattle, you can get them if you have the right biome for them.
4. Provide as many Alternatives as possible. This is part of 'dynamic resources' mentioned above. If you don't have Horses, chariots can be pulled by donkeys or hybrid donkey-hemippe animals. Horseback-Riding (if kept in the gam) on the other hand, requires Horses, but early mounted units are not necessarily Game Changing: the relatively horse-poor Britons got along quite well with chariots and infantry hordes right up until the Romans overran them - with more infantry. Likewise, for minerals, Silver and Gold can be considered interchangeable as Luxury items, Dye materials range from coastal shellfish to jungle plants to minerals, and Ivory can be obtained from elephants or walruses - from completely different climates and terrain.
5. Almost all of the 'natural' animal and plant non-food resources can be replaced by manufactured alternatives between the Renaissance (Early Modern) and Modern Eras. Niter is an early example, originally obtained from farm animals and natural deposits, then 'manufactured' in Nitraries. Natural Dyes have a niche in craft work, but modern Dyes are almost all chemically artificial. This is part of the Alternative Resource concept above: as your requirements change and quantities required increase for your Civ, your alternatives to digging them out of a given hunk of ground should also change.
These concepts would make the 'resource game' more complex, because you would have to actually pay attention to it throughout the game. But it would have to be better than the current system where every copy of a resource appears at the same time and Never Again, and all resources are static and unchanging throughout the game regardless of your technology and requirements and needs.