> Emergency measures being valid for the duration of the emergency would be pretty straightforward.

Deciding when the emergency is over is less straightforward than a fixed time period. A government that wanted to extend the measures indefinitely would just claim there's still an emergency.

For example the Patriots Act in USA, signed into law after 9/11 attacks. The sunset was in 2005, but it's still in force.

But the cooperation of legislators is required because of the fixed deadlines. If the government would be allowed the right to extend the provisions on their own, they probably would try to do that in perpetuity. With a legislative branch that actually cares about civil rights, the former is the much better option.

Not straightforward - somebody would have to decide when the emergency is over, which then becomes a political question.

And even if the emergency is not over in a year, it makes a lot of sense to reconsider if the measures (which were decided very quickly) are actually appropriate and necessary going forward. Hopefully a lot have been learned in a year.

I think it's because it makes them able to react much quicker if hit by a second infection wave

You are forgetting to factor in complacency. When is the second wave? when should we stop waiting for it? that just depends on how useful the law is for those in power.