[muti]

Non consecutive isn't surprising, any consecutive Fibonacci numbers in the sum can be replaced with their sum, which is itself a Fibonacci number by definition

[lupire]

That's not sufficient to be unsurprising.

What if a sum has more than 2 consecutive Fibonacci numbers? That doesn't cause a problem, but it takes a little more work to sort it out.

[muti]

I find the distinct property much more interesting and non obvious.

It looks like non consecutivity is only there to force unique solutions hence called zeckendorf representations