Start button takes its sweet time

Crayon

The car and your key-fob do an encrypted RFID handshake. This involves passing of public/private key pairs with known lists of "correct" challenge/response pairs. This involves quite a bit of back and forth between the key and the car, as well as range verification and such. This isn't the entirety of the extra time needed, but it's a chunk of it. I'm sure the rest is the ECU checking vital sensors/systems before startup.

It's a disadvantage to not having a physical key. With a physical key, you don't need encryption, as the key itself serves as the same layer of protection as the encryption. Thus, physical key = much faster.