Eyeletted rims seem to have fallen out of fashion. My 7 year old Mavic tandem rim that recently started cracking at the spoke eyelets had double eyelets. I assume that the theory behind the inner eyelet is so that the spoke will also pull from the inner rim web. My Velocity Fusion replacement rim doesn't have any eyelets at all. Who can explain the reasoning behind this shift?

May 2005 the Mavic MA40 rim (hard-anodized, double-eyeletted) on my rear wheel started cracking at a few of the eyelets, espcially one of them, going badly out of true. I replaced the wheel. Perhaps due to too-high spoke tension when I'd rebuilt the wheel with new (straight-gauge) spokes some years prior, and the hard-anodizing certainly didn't help either.
But my new wheel has an Open Pro rim, with double eyelets as well.

But your larger question: has there been a trend in rim design/production toward not using eyelets?
And I'm not sure on this. There are three categories really: double eyelets, single eyelets, and no eyelets. Rims can be designed and produced well in any of these configurations, although high-end rims are usually double-eyeletted or have no eyelets. So there are multiple directions that a trend could go.

Eyelets help to spread out the force of the spoke's tension over a wider area of the rim, and also provide a stronger surface for the spoke nipple to rotate against when under tension. (Some wheelbuilders use washers between spoke nipple and rim interface when building with rims that don't have eyelets.) With single-eyeletted or no-eyeletted rims the force of the spoke tension is borne by the outer wall of the rim (although some aero rim designs are different). Double eyelets spread out the force over the inner and outer wall of the rim, meaning that the rim is stronger or that the rim walls can be lighter.

I suspect the trend away from eyelets has to do with the trend towards "aero" profile rims. I suspect that the trend towards "aero" rims is largely due to the improved visibility of the manufacturer's name and model number on the sides.

And I suspect you're right on both counts...

The mechanics of aero profile rims not needing eyelets is because the a-frame shape of the rim doesn't need reinforcement the way that a flat or box-section rim does...
That said, I've seen plenty of aero-profile rims that have cracked where the spokes go in.