Otherwise they will go bankrupt and quit being able to make Sims.
While EA's customer support is lacking, they are second to none when it comes to promoting a franchise. Madden (as well as their other numerous sports franchises) and Need for Speed alone could keep them afloat for a very long time. Even Spore, while it was somewhat poorly received to start with, has developed a very loyal fan base and has done well enough for them to continue that franchise recently.
But, it's likely that EA would look to sell The Sims franchise if it started doing poorly. It's a solid concept with a loyal fan base, even if that fan base is a bit annoyed at the moment. While Sims 3 would most likely be a complete wash-out if that happened, it's probable that whoever bought it would try very hard to avoid the mistakes that EA has made and is making when releasing Sims 4. So all is not (completely) lost.
But this digital only thing isn't going to happen overnight. It's not likely to even happen completely within the next year. It's going to take a long time for them to try and ween gamers off the idea of having a physical disc, if that would even be possible at all. It's even possible that if public outcry was loud enough that they would change their minds.
Me too, really. I haven't even heard about EA before I started playing Sims seven years ago. Sure, who hasn't heard of Battlefield, but I believe Sims is their greatest creation - that's the reason it sold 130 Million copies in ten years.
The Sims is
not their creation. They gained custody of the franchise by buying out Maxis, the company that created it. The reason it has sold 130 million copies is because it already had a huge fan base, who was used to problems being fixed quickly and permanently. This is why a lot of simmers are hot under the collar.