Technologically, sure, we could ship games on the same type of flash technology used in SSDs. Heck, we could even put the SSD controller inside the machines, and make it configurable such that each game could choose the number of flash chips (channels, which is part of how SSDs attain the speeds they do), and capacities to meet their needs. But even if your performance/capacity needs are small (say, small games that don't stream content in) you're talking several dollars just for flash, maybe another dollar for circuitboad/shell/packaging, and because you're now physical-only, lots of marketting spend to gain a small amount of time on a small amount of shelf-space -- oh, and you've also just raised the pricing floor beneath which you can't profitably sell.
Selling new games at retail is already a thin-margin endeavor (a retail outlet makes perhaps a couple bucks per unit) -- that's why Gamestop pushes you to buy used copies of even the newest games: their profit margin on those is much bigger, even at 5-10 dollars savings for the consumer. Big retailers like Walmart only really sell them as a sort of attraction, in the same way that gas stations sell milk -- when you need milk, if you can get it at a convenience store, you might also make some other higher-margin purchases. In both cases, that's why the milk and the games are always in the back of the store.
There's just no room to change the production cost of the tangible good from pennies to dollars. Would the market adapt to a higher price? sure, mostly. But from the perspective of the publishers and studios, all they'll have succeeded at doing is convincing their consumers to pay more for something they see non of the profit from, and now you have less money to spend on the next game, which they would see some profit from.