Mythbusters failed because they were having a hard time aiming them all accurately. It can be done, but only if you know the tricks to it, which they didn’t.
And it’s not particularly a “Greek story”, either. The feat is often attributed to Archimedes, but while he did make many weapons, that wasn’t one of them.
In battle, the flaming arrow might be more effective. But in war, the solar reflector would be.
A large part of Archimedes’ actual success vs. the Roman Army was that the weapons he invented were so far beyond the Romans’ understanding that they ended up terrified of everything that they couldn’t instantly recognize. And if you’re a classical-era soldier, and your enemy is somehow making a whole hillside appear to be ablaze and suddenly your ship is burning without anything ever even touching you, you’re not going to particularly care that the blazing-hillside weapon isn’t actually as effective as a pitch arrow; you’re just going to do everything you can to not have to fight them.
As well, the range of a flaming arrow is a couple hundred yards. The range of a mirror weapon on a clear day might be a mile or more.
Even now militaries are very excited about the advantages energy-based weapons will have in range, time of flight, and ease of aiming vs. more traditional “kinetic” weapons. And, just as Archimedes found in his day, stable aiming over the time required to deliver enough energy in one spot to really matter is just about the longest pole in that tent.
Obviously, you didn’t read the thread because this has all been discussed. And Mythbusters did achieve a small flame, on about the third attempt.
In reality ships roll, pitch, and move, and that combined with it being relatively hard to aim in the first place would make it a practical impossibility.