The reason for switching to ECC is speed and key size. The NSA recommends 3096bit rsa keys for 128 aes, but only 256 bit ecc keys for the same security against traditional attacks.
They also went ahead and recommended 348bit keys for ecc, but I don't know if something like that is widely used anywhere. Curve448 is nice but slow. Curve41417 is fast but largely unused.
Honestly impressive.
On a related note, someone might discover some elliptic curve math tomorrow and your CPU can break all that stuff just as well...
They chose to standardize a version that's secure against attacks that only they knew at the time, shorten the key length so they can still brute-force it if they really need to, and successfully kept the attack secret until researchers at a foreign university independently discovered it decades later.
As soon as quantum computers have enough qbits prime factorisation can be done very quickly. Not sure the timeline on that as there are a lot of challenges in the technology and it is hideously expensive, but a lot of the move away from RSA to elliptic curves is driven by readiness for quantum computing.
tl;dr: not in our lifetime.
