Board game design opens up some opportunities for pure art: things that have almost no impact on the gameplay, but have a design nonetheless.
Imagine a game in which you build buildings. Each building costs resources to build, and there are four types of resources — let's call them A, B, C, and D. The resources aren't strongly thematic, or tied to certain game mechanics. They're just four resources.
How do you cost the buildings? Do you restrict yourself in any way, or does each building just cost just a variety of different resources?
Creating a hodgepodge of every possible resource combination isn't what I do, in this situation. There's a kind of aesthetic beauty you can enable, by constraining yourself. You can create structures and rules, to make the game components seem like they're part of a logical system. You can establish your own rules, and then make a few cards that break them.
In the example, you could make the basic buildings cost ABCD. You could make another group that costs AABB, BBCC, CCDD, DDAA etc. A completed pattern like this is called a cycle. You could generally restrict your costs to four or six resources, and omit three and five, or use five only for a single cycle of AAAAA, BBBBB etc. buildings. All this logic and symmetry makes the game look like a structured and meaningful thing, not just a pile of game elements. It sets up expectations. Someone who has seen the AAAAA, BBBBB and CCCCC buildings will be interested to see what the DDDDD building is.
I haven't even touched on running cycles and patterns through the actual function of the buildings. That's absolutely something I would do. Applying meaning to each resource is another level of structure I would add in. Maybe buildings costing any "A" are the community buildings, useful to everyone, while buildings costing any "B" are the economic buildings.
Structures are not just art. They also help with comprehension. If I dealt you a hand of seven of these buildings, and they had costs like AAAB, ACC, and BCDD, you wouldn't be able to recall what was what, because it would all just be random. You'd have to constantly check the costs. If, on the other hand, all the cards cost ABCD, or various XXYY combinations, it would be much easier.
Look at all your numbers and combinations, and add order and meaning to them, even if you don't have to. It's worth sacrificing a small amount of design space for.
In Radlands, "person" cards mostly cost one water to play. These are themed as generic people, like "Sniper" and "Scout". There are two of each. A few people cost three water, and have very large effects. I decided that these would be themed as unique characters, with personal names ("Molgur Stang" etc.), and only one copy of each. There is no rules difference between the generic and unique people. It's just cool and thematic.