Ramming speed was not, in fact, the fastest speed available, but rather the fastest speed that you could ram your vessel into another, and expect to still leave your ship in reasonably sound condition.
Galleys are moved by muscle power in combat, and as such, are built lightly (muscle wears out quickly under combat conditions!) to facilitate speed and handling. A successful high-speed ramming attack, while being very deadly to it’s victim, risks leaving the rammer with sprung planks, a broken forepost, a damaged keel, or a lost beak (this happened at least once during the American Civil War, IIRC). Worse, a full-on ram attack risks leaving the rammer entangled with it’s victim, which pulls both vessels to the bottom.
The tactic was to ram a speed that approaches a fast walk, but to back oars just before impact, puncturing the lightly-built hull of your opponent, but already begining to disengage so that your beak is quickly removed from your opponent’s hull, lest they board you, or more likely, they sink enough to bind-up your beak in the opening and drag you to the bottom with them. Needles to say, this was a hard tactic to achieve. Far easier to run at high speed parallel to your opponent, shipping oars and cutting in close to them at the last moment, to try and catch them before they can ship their oars, thus breaking their oars (the butt ends of which would flail about the oardecks like murderous threshing machines). Meanwhile your archers, slingers, and and other ranged weapons would try and off the opposing command crew, especially the steersman. Fire was (rarely) used, as were large stones, darts (NOT pub darts, but big nasty things!), arrows, spears, slings, and a host of assorted nastyness. Once the opposing vessel was ‘decapitated’, it was easy prey. Meanwhile, the opposing vessel is doing it’s level-best to return all the favors, and then some.
You can see why many such contests became infantry fights accross wooden decks. It’s easier to train and pay for good infantry than it is to pay for and train a good navy, and far simpler to just grapple and board than to try fancy tactics (especially late in the fight, when the oarsmen were exhausted).
These boats you are talking about were Greek, not Roman. A famous battle where this happened happened at (I think!) Piraeus. The Greek trimeres had spurs installed at the bow of their ships so they could effectively ram the opposing Persian ships. And yes, this is where Greek Fire was used.
