@Hanako Ikezawa: Yes, and I bet we're not going to shoot at one meteor, asteroid or comet (or, more importantly, have those things referenced).
If this is a casual - "We're a bloated society with nothing better to do than invade unexplored regions." like Europe in the Age of Exploration. Sure.
If this is a - "We're fleeing from the destruction of our entire galaxy, way of life and civilizations." Where even the impossibly large Ark is at LEAST fitting two species currently (Krogan and Human) and likely no less than six (Krogan, Human, Asari, Turian, Salarians and Quarians) - then I find the believability of having enough ordinance to have epic space combat to be very low.
Let's say there's populations of 10000 for each species (ludicrously large populations to be floating in a can - but let's play science fantasy). That's very likely at LEAST 60000 people (men, woma - elderly, children and the fully functioning). The amount of space... food... clothes... medicine... entertainment... manufacturing... and exploration (which would include things like R&D, fleets outfitted for exploration missions over combat, quarantine and decontamination, etc) - would, to me, far out way the space battle relevance.
Evasion would be FAR more pragmatic than "standing your ground". The Ark isn't carrying militants... it's carrying civilization.
NOTE: Battlestar Galactica is a good model... and yes, of course, that was a military vessel that protected a fleet of civilian ships - but they spent nearly all their time evading. The Ark... is not the Galactica. It should NOT be staying behind to make valiant stands... as it, at least as far as we know, is all that remains of the Milky Way species.
Yes, I'm aware this is science fantasy... and that demands man vs. other conflicts... but I'd love a game that gives an honest go to man vs. nature and/or man vs. self. Not yet popular with the video game crowd - but growing (with games like The Long Dark) for example... (a game which is still ludicrous in its premise simply to make it more exciting).