Is I2C actually that different?
Yes. I2C is a much more complete protocol than SPI.
eg. An I2C slave can hold the SCL line low when it detects a start condition. This puts the master "on hold" until SCL is released. The Tiny85 has a hardware latch for this so the software response time is never an issue, it can take as long as it needs (within reason) to respond to the start condition, set up the USI to receive the data, then release the master to send the data bits.
I think the start-condition detector can even wake up the chip from sleep mode. You can be sleeping and still respond to I2C transmissions.
(See bits 4+5 of the USICR register for details).
I2C has other problems, and is generally run slower than SPI,
You don't have to go at 100kHz if you know you're talking to a Tiny85 @ 8MHz. The Tiny85 hardware will work much faster than that.
A limitation of i2c is the number of addresses
Needing a separate slave select pin for every SPI device seems like a bigger limitation to me.