This is already happening. Not perfect data, but if I look
here, it appears that only about 19% of games get a physical release.
There's some math attached to that. What does a cartridge cost to manufacture and what percentage of manufactured cartridges need to be sold to break even? How many copies won't they sell if they only have a digital release?
Also, the manufacturing is an up front cost.
I suspect only the games expected to sell really well will get a physical release. I think Nintendo continues to support a cartridge slot until they have a reason to break backwards compatibility anyway. I could speculate at reasons they would, but that's beyond the scope of this answer.
EDIT:
To add to what I said above, a blu-ray drive is expensive and problematic compared to a cartridge slot. A cartridge slot has all it's costs in developing the electrical interface and sealing the slot against dust intrusion. The silicon cost is probably negligible. If I'm just looking at pcpartpicker (not by any means authoritative, just a ballpark) a bottom end blu-ray reader is about $70. Best Buy shows about the same for a bottom end player. The cost is flipped for media. A blu-ray disk and packaging is probably under $2. A cartridge is linked to the capacity of the cartridge, but it's probably going to be above $10 in any case. Someone else can fill in if they have better numbers.
Sony and MS have an incentive to drop their blu-ray drives in the cost to manufacture. Publishers have incentive to stop selling on physical media in the cost of media. Nintendo doesn't have an incentive to drop the slot, but may start picking and choosing which games they publish get physical releases.