I used never to have a problem - even when Silver. Generally if seats were still for sale then they'd be available for reward tickets.
It seemed to change around 5 years ago for me. Non-availability was the order of the day. Eg on London, perhaps in 10 days there would be 1 or 2 flights available. The rest you'd be waitlisted. On TPE-HKG, often the only flights available would be at the end of the day. TPE-SGN is also very patchy. These are the only routes I know well.
This waitlisting happens whilst in some cases they are still selling the most discounted tickets.
But that's not to say you won't get the seats you want. It seems EVA just resent giving away something "free" if someone might pay for them. Often waitlisted seats will indeed clear, perhaps a few days before the flight. That's a pain if you are trying to plan something.
I can well believe ak333 doesn't have a problem - I think Diamonds are sufficiently few that they will get better treatment. Perhaps other routes are better than mine.
Everything I've read suggests to me that EVA is not particular bad, it's just they used to be so much better. I wanted to use some Air France miles to fly CDG-SGN in business class. Months at a time were blocked out. It was 2 or 3 years before I could get flights that made sense to me. AND I had to pay a fee when I had to change the inbound portion - something EVA doesn't do. I still have a load of *alliance miles that I've had several goes at using but to no avail.