Sword & Shield will survive.
Pokemon games have always sold very well despite whatever happens. Game Freak pulled this move before, and Ruby/Sapphire still sold as well as any Pokemon game after the first two generations has. Black/White was, around the time of its release, a very hated Pokemon game, yet still brought in the typical sales numbers for main series Pokemon games. Sun/Moon, despite legit being an unfinished beta version of US/UM, still sold well too.
For as many people who are angered by Game Freak's decision, there's as many people who are not and will still buy the game(s). I know I'll still be buying a copy of Sword or Shield. I probably shouldn't, given that SwSh is likely to be the same unpolished rehash bait-'n'-switch that Game Freak has been giving us since Gen 3 that I and others have gotten very tired of and I should just wait for the inevitable announcement of Pokemon Laser Sword and Pokemon Energy Shield, but I'm probably also mildly insane. The fact that some Pokemon are not in the game, period, does not bother me personally. I don't really breed or competitively battle anymore (and if I ever make a return to it, it will be almost certainly be exclusively on Showdown/battle sims), so outside of a few special Pokemon that I'd like to use forevermore, the decision does not particularly affect me.
Which, for those wondering why this is such a big deal for some people: a lot of people have reasons important to themselves for transferring (large numbers of) Pokemon to the next generation every generation. Some of those being for breeding/battling purposes, or they're just really attached to having a specific Pokemon/species of Pokemon always available, among other reasons.
Pokemon has long sold off of its name alone, and I don't think that even this will change that (though we'll see what happens). If Game Freak's smart (from a purely businesses standpoint though), they will patch the game. Not with all the remaining Pokemon though. Just a handful every couple of months to bait people back into playing or buying the games because their favorite(s) are now in the game, and give (potentially false) hope to people, make them think that maybe one day the Pokemon they want will make it back in (even though it might not). Then can also claim that they "listened to the players" despite not exactly really giving what people wanted.
They are also fortunate that they announced this now instead of much closer to release. Gives people time to simmer down, as well as give them time to reveal other things that might entice them into buying SwSh.