"...can pick up the signal from keys..."
"...can pick up the signal from keys and copy them to the car, unlocking them and disabling the alarm system."
We need to clear about this. Especially considering system design as impacted by limited battery capacity.
Your car key isn't like a smartphone, needing to be recharged every night. So it cannot be emitting RF signals all the time. The tiny button cell needs to last a year.
Your key fob remote control (older RF technology) would be activated with a button press, and can thus have long range. So it can be captured surreptitiously from across the parking lot. It needs to have basic security like rolling codes (if somebody grabs the code out of the air, it's already stale). My ten year old Mercedes has rolling codes, just like the 1999 model I had 18+ years ago.
Note: The rolling code algorithm needs to be kept secret.
Keyless Car Starting is probably using RFID. That's much shorter range. The hackers need to get within a meter or two of your keys, so their can 'illuminate' it with enough RF to power it up. The system designers should include some handshaking, not just an easily copied serial number.
If the researchers have identified a make and model of vehicle where they're using RFID relying on just the tag's SN, then name names and inform the Insurance industry. Such cars would be immediately recalled and lawsuits would fly.
I detect that these researchers are exaggerating. There's no mention of the fact that many vehicles already have excellent security.
Those that don't should be punished via theft insurance premiums. It'll sort itself out quickly.