What in the world are you talking about? The GBA launched at $100. Just $135 in 2015 dollars.

Point being, the U.S./NA market was grossly inflated, and even had they waited a couple of years to release the DS, the U.S. market would still be disproportionately large compared to the rest of the world. I have annual NPD data for handhelds going back to 1995:

We see that huge spike with the GBC continuing on through the GBA, and then it just got bigger with the DS Lite and the addition of a successful non-Nintendo system. This is more or less congruent with shipment data for the whole region, which showed a huge and continuous boost from the very late 90s on throughout the first half of the 00s.

Now let's look at Japan.

I don't have sales data prior to 2000, but shipment data for Japan suggests far more modest growth of Nintendo handheld sales, hence why the GBA only sold half as much as the original Game Boy line. But the overall handheld market has remained quite strong, though interestingly the DS had a less protracted period of mega-sales.

As for Europe, VGC is the only place that has actual sales data, but shipment data (which includes not just Europe but also Australia, Oceania, and various other minor markets) suggests that the GBA was doing not noticeably better than the Game Boy line was in its best years, and that the brief period the GBC was around it was selling faster than the GBA ever would (though Nintendo could have just dumped a bunch of them on the market to deal with the Pokemon boom). The DS was just as huge in Europe as it was in America. As for the 3DS, shipment data suggests it is lagging behind the GBA, but only by about 15% or so, but the 3DS did have a weak start, and lost momentum is hard to recover from. It's sufficiently close to where factors endogenous to the market can explain the difference.

The U.S. is still the anomaly here. The handheld market in the region became absolutely monstrous beginning in 1998 and didn't lose any steam at all until 2012-ish. We simply did not see the same thing in Europe and Japan, hence why the GBA sold only half as well as the original GB line in those regions but almost beat it in America, and NA representing about half the GBA's sales, the biggest regional share by far of any major handheld. This is why I think asking why the handheld market was so big in the U.S. back then is an even more pertinent question than why the 3DS isn't doing as well as the GBA in the region. For Europe and Japan, once the market got out from under the DS's massive shadow, it was back to business as usual.