Floating numbers on the screen should always be the last resort. XD Seriously though, if you are investing into pretty graphics because you think it sells, why invest into floaty numbers to spoil the graphics because you think most players will be the kind of hardcore that doesn't care about visuals when they can get feedback?
Besides, not knowing where that good hit came from is not achieved by floating numbers either - those are also just a visual cue near the target, so if you want to give the player a way to see which of their ships did what to the enemy, the only practical suggestion so far would be Xankar's logbox, since that could note "Plasma Weapon from Ship X Formation Y did 33/99 damage to Enemy Z from formation Q", which is definitely too much to show on a screen. Even if you make damage recieved floaties over the enemy, damage caused floaties over your ship, and have a sound signal for good measure, with color-codes for every weapon and shield type, you would just make even more visual clutter and not generate any more overview or control.
There should be visual cues for (random) critical hits, such as the flashing hitbars I suggested, but to really generate oversight of weapon effectiveness, you need more than that, I realize now. Coming back to a reel or other marker on the enemy formation/ship that shows, yes, this ship was hit by a plasma weapon, and it was not very effective (plasma bolt with a thick red downward arrow across it, floting next to the hitbar). You will probably remember which of your ships have plasma weapons and should look for another target, if you don't think players will, just put another symbol (plasma bolt with an orange exclamation mark) next to your ship's hitbar, give a more generalized visual cue (circle with red bar, denoting fire in inefficient) and possibly a sound cue, "Weapons Ineffective" (which will be annoying, so don't do that).
edit: This does not seem to create a lot of discourse...