I've had this question for a long time. When my gearing is a little weird, and the chainring is barely touching the front derailleur, I see that the chainring oscillates in distance with respect to the FD, as the crank rotates. Is this built in on purpose, or is it the aluminum giving in to fatigue?

Probably neither, although it is possible to bend a chainring by pedalling hard.
Most probable cause, unless the chainring has gotten dinged sideways somehow is simply manufacturing tolerances.
The crank might not sit entirely perpendicular to the BB, or the chainring flats on the carrier aren't machined to the exact same level, or the chainring spacers aren't exactly the same size, or....

Your options are:
- ignore it if it isn't affecting shifting
- remove the chainring, check that it's flat. If it isn't, attempt to straighten by use of rubber or wooden mallet, or by bending.
- If the chainring is flat, shim the chainring flats on the carrier until frustration or the desired degree of trueness is ahcieved.

Do they look like this?

Biopace Chainwheels

derailleur chainrings are made to be either outers or inners

If it's moving side to side slightly, it either was always that way due to manufacturing tolerances as Dabac explained or the support arms got bent long th way by a crash or other impact, but not from simply riding.

But, as I suspect, you mean the radial distance to the cage varies, there are a number of possibilities to explain variation in the 1-3mm range.

1- you might be seeing the shorter teeth that are part of the shift gates (my term) which are intended to make shifting easier. There are usually a pair on the outer ring.
2- the same manufacturing tolerances as above.
3- if your rings are mounted supported by the bolts and do not have a supporting shoulder on the arms, they can shift slightly causing them to be eccentric. This is often an issue on single speed bikes and can be corrected by loosening the bolts slightly and tapping the highest spot toward center. This is a bit of a trial error method, and will take some time to get the ring centered well. It's useful for single speed, but you needn't bother on a derailleur bike because the eccentricity doesn't make a difference.

If the variation is much more than a few millimeters, then you probably have BioPace or some other ovalized rings as suggested above.