Should video cables come with a new video card or monitor?

With neither. Some setups need HDMI, some need DP. Why waste putting extra cables into a box that would end up laying in a junk drawer?

IMO, Monitors since they will ultimately display the image. The HDMI and Displayport cables should match the specifications of the ports. It should include a single 6ft cable per port.

For example, if the monitor uses HDMI 2.1b ports, it should include an HDMI 2.1b cable.

Older GPU
If an older GPU has HDMI 2.0 outputs, the 2.1b cable will still work, but will only work as run at the GPU's 2.0 bandwidth.
Newer GPU
If later in the future you upgrade to a GPU that has a theoretical HDMI 3.0 port, then it should still output to the monitor, but only at HDMI 2.1b speeds. That monitor will never work at HDMI 3.0 speeds, but it should be able to fully reach its own HDMI 2.1b specs.

That is such a huge waste of material.
When a monitor supports both display port and hdmi port, they need to supply 2 6 foot cables just in case? And what happens when 6ft isn’t enough for a specific situation. You need to then buy an extra one just in case?
Also, when buying replacements, the cables are totally unnecessary.
We have a bad enough problem with E waste. Making it worse for the sake of the tiniest convenience for the average consumer is ridiculous.
- 2 cables for a monitor that will be used for about a decade or so, with a length that is typically long enough for any desk setup so that you don't have to trial and error cables types/lengths will probably reduce the amount of cables that the user will end up ordering.
  If the monitor comes with no cables, someone might end up ordering a 3ft HDMI 2.0 cable, which ends up being too short. Then they'll order a 6ft HDMI 2.0 cable, which is the correct length, but isn't the correct cable to fully utilize that monitor. Then a few years go by and they upgrade their GPU and realize that their monitor isn't displaying to its potential, so they finally order the correct 6ft HDMI 2.1b cable.
  Ask me how I know that has happened before 😂 (it was me).
Well put.

With the monitor. otherwise you'd have to ship GPUs with a variety of cables, without knowing which and how many of the type the user actually needs, and which are just e-waste

No, that's just pointless e-waste.

Couldn't you make the same argument with phone chargers?
- Not well, since those are easier to move and used for a variety of devices.

They often do come with monitors, and at least in office installs they often get thrown straight back out again as the monitors are put in (the bases commonly get tossed as well due to fitouts using monitor arms).

No, mainly because we are at a point where cables have standardized to a point where it is easy to find a compliant cord on the secondary market. At that point, there are decisions made by the consumer which are going to dictate what kind of cable is needed, like required length.

And cables keep piling up! I'm drowning in them. Seems like a waste to just throw them out.
Same with those damned allen wrenches that come with... everything. I have so many of these damned things.
That is definitely not true for DisplayPort. If you need anything beyond DP 1.4, the cable market is a minefield. I even encountered a monitor that was straight up incompatible with DP 2.1. Would not work with a new graphics card, while HDMI still worked fine.

monitor because it's max specs define what cable you need.

Are you asking inclusive OR, or exclusive OR?

EG, should your question be interpreted as "Which of these should the cable come with?" Or "Should these even come with a cable?".

I thought OP was asking the reverse question: if I buy a cable, should it come with a monitor and/or video card? But of course that would be insanity.
I think you're confused about what inclusive and exclusive OR are. They both generally refer to boolean operators (ie, the answer must be yes or no).
If I interpret the question as inclusive OR, then I should answer yes if and only if I believe that cables should come either with a monitor or gpu or both.
If I interpret it as an exclusive OR, then I should answer yes if and only if I believe that they should come with a monitor or gpu, but not both.
Your examples have nothing to do with inclusive vs exclusive OR.
- The concept of "inclusive or" in language is a bit different than that used in boolean logic.
  The simple case is: "would you like chips or salad?" "Yes." Vs "Would you like chips or salad?" "chips".
  In this case, it's unclear whether the question is: "should a video card or monitor come with a cable?" "Yes" Vs "Should a video card or monitor come with a cable?" "Monitor".
  The two examples I wrote were attempts to reframe the question in two different ways to avoid that ambiguity.
  As you pointed out however, OP wrote the question backwards, in a way that could be interpreted in a third manner, where buying a cable includes a video card or a monitor.

I could swear that they came with new monitors which is standard.

New video cards should come with any extra peripherals needed to make it work with said monitor or whatever features that was advertised.

They do come with monitors. I bought a new one like 6 months ago

They should be optional, just like power cords.

My environment is at a lack for cables, for administrative reasons, except for power cables.

Like HDMI and VGA cables? Or those analog ones for older TVs? Why would either type come with a monitor or card if you just bought the cable?? Have I misunderstood?

I think they are asking, if when buying a monitor or video card, should that come with the cables needed.

Monitors from memory.

If the ports are updated to a new standard and you need the new cables to get maximum throughput, yes.

If they are the same ports as previous cards and the old cables work fine? No.

Printers are one of those things that has never come with a cable. I remember even back in the 90s, you'd buy a new printer, and they'd ask "do you need a printer cable too?". Back then they were parallel port cables, but the trend continued when printers adopted USB.

I always thought it was a blatant upsell conduit. Of course I need the cable. Can't use the printer without it!

These days however, I've got so many printer cables including parallel port, USB-B, and ethernet, but I mostly print via wifi. Now I'm glad they don't come with cables, and same with graphics cards, and even mobile phones.