I have a passing interest in classical naval warfare and my assessment is this (for what it's worth).
For big fleet actions I would split classical galley warfare up into three periods.
1. Greek Vs Persian and Peloponnesian War. Aphract triremes, almost exclusively. Fleet and squadron actions a plenty.
2. Successor, Mid Republic / Punic War / Rome Vs Successor. Ships are getting bigger. The Successors are using plenty of bigger ships (quadriremes, sixes, tens, etc.), and triremes become scouting ships. The Carthaginians invent the quinquereme, the Romans copy it, and this is the main battleship for the Punic War period – there are some smaller support craft and a few sixes though. The successors are still using bigger ships. Ships are big enough to mount towers and engines. Almost all ships are cataphract. Tons of stuff here.
3. Roman Civil Wars. Rome is still using the Quinquireme as the main battleship, but is also starting to develop smaller ships to patrol what is quickly becoming a Roman lake. These are the liburnians which will soon be the dominant military vessles in the Med'. At Actium, Octavian uses a mixed fleet of quin's and liburnians against the last Successor fleet under Antony and Cleopatra containing quin's, and several much larger ships. If you have ships for 2 above, you just need to add liburnians. Not that many actions here, Actium being the stand out famous one.
After Actium the Med' is, as stated, a Roman lake and big ships are no longer required. The Romans just need fast, cheap patrol vessels to catch pirates, etc. The liburnian is well suited to this task. Therefore, IMHO, the statement is TRUE.
Of course, tactics too changed over the period, which puts a different slant on which sub period is best. Personally I like 2 and my ships are aimed at that periods, but I have a few aphract triremes for doing the earlier stuff (at squadron level) and use some biremes for liburnians for the later.
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