ATtiny13 at 16MHz? Why not?
It’s all in the datasheets!

The ATtiny13 can be driven by an external clock signal (by programming CKSEL with 00) but it does not have its own crystal oscillator.

You would need external circuitry (crystal, inverter + some capacitors and resistors) to generate the clock signal and drive the CLKI input (pin 2). You would not be able to use that pin for other purposes.

The ATtiny25 and 85 have the ability to directly connect a crystal (plus some capacitors) and drive it directly, BUT it needs two pins (2 and 3) on the chip, which is a lot for an 8-pin device.

So you need to define what you mean by “Hassle”, if you really need the performance and can live with the downsides.