Luthien didn't show any offensive capablities. In the quest of Beren and Luthien, she was protected by Beren and Huan.
Lets dismiss the idea of ordinary soldiers defeating Wizards and such, since that is just a recent consept. Cyrus was not an ordinary soldier. He was the greatest soldier of his time, the hero of his kingdom. Eomer may not be able to defeat someone like Galadriel, but Aragorn may have been able to. Anyway, that is a moot discussion. Fact is, people believed that Cyrus would defeat Magus, although Magus was too great for him and his legendary sword. Thats enough for me to grade him as a possible epic hero (not saying he is one, but if he defeated Magus, he would fit that catagory).
For your second point, I concede that you may well be right. Cyrus may indeed be some sort of well-known hero, perhaps a tragic hero of a sort. It is never fully explained. Thus he may have greater strength than is made manifest. On that one day, however, he was caught unawares by two: Magus and Ozzie together. Even if he could have victored over one, the two overbore him. So, like I said, I will bow to you on this point regarding Cyrus, now.
But for the first one... well, you're wrong there without doubt. Firstly, as an adherer to the Tolkienesque school of fantasy, I take any sort of rule-based magic to be strange, and in CT only the effects of game mechanics. Thus someone's power cannot be classified solely into defensive and offensive. She may be better at one or the other, even as a fighter may be better at taking hits or giving them... but a fighter has fists regardless, and can at least to some degree both give and take blows.
Perhaps more importantly, though, using your defenition, you are wrong. Luthien does, on more than one occasion, use offensive magic. For your consideration:
Now chanting clearer down she cast
her long hair, till it reached at last
from her window to the darkling ground.
Men far beneath her heard the sound;
but the slumbrous strand now swung and swayed
above her guards. Their talking stayed,
they listened to her voice and fell
suddenly beneath a binding spell.By her power she cast sleep or binding upon her Elvish guardians, and escaped them. Later, at the doors to Angband:
when, lo! a marvel to behold:
some power, descended from of old,
from race divine beyond the West,
sudden Tinuviel possessed
like inner fire. The vampire dark
she flung aside, and like a lark
cleaving through night to dawn she sprang,
while sheer, hear-piercing silver, rang
her voice, as those long trumpets keen
thrilling, unbearable, unseen
in the cold aisles of morn. Her cloak
by white hands woven, like a smoke,
like all-bewildering, all-enthralling,
all-enfolding evening, falling
from lifted arms, as forth seh stepped,
across those awful eyes she swept,
a shadow and a mist of dreams
wherein entangeld starlight gleamsAnd yet before the throne of Morgoth:
Down crumpled Orc, and Balrog proud;
all eyes were quenched, all heads were bowed;
the fires of heart and maw were stilled,
and ever like a bird she thrilled
above a lightless world forlorn
in ecstasy enchanted borne.
All eyes were quenched, save those that glared
in Morgoth's lowering brows, and stared,
in slowly wandering wonder round,
and slow were in enchantment bound.
Their will wavered, their fire failed,
and as beneath his brows they paled,
the Silmarils like stars were kindled
that in the reek of Earth had dwindled
excaping upwards clear to shine,
glistening marvellous in heaven's mine.
Then flaring suddenly they fell,
down, down upon the floors of hell.
The dark and mighty head was bowed;
like mountian-top beneath a cloud
the shoulders foundered, the vast form
crashed, as in overwhelming storm
huge cliffs in ruin slide and fall;
and prone lay Morgoth in his hall.If that's not a mighty offensive power, I don't know what is. She laid low the great Dark Lord himself, the devil in his very hall.
And finally, at the bridge of Tol-Sirion:
Lo! by the brindge a gleam of light,
like stars descended from the night
to burn and tremble here below.
There wide her arms did Luthien throw,
and called aloud with voice as clear
as still at whiles may mortal hear
long elvish trumpets o'er the hill
echo, when all the world is still.
The dawn peered over mountains wan,
their grey heads silent looked thereon.
The hill trembled; the citadel
crumbled, and all its towers fell;
the rocks yawned and the bridge broke,
and Sirion spumed in sudden smoke.Well, if that's not mighty offensive power, I don't know what is. No one else I know of, not Gandalf or even Feanor or Turgon are spoken of as wielding such overmastering power. Even faithful Finrod Felagund loses in a battle of wills against Sauron, whereas Luthien lays low even Sauron's dark master Morgoth.
And, if you mention Galadriel... well, it does say that, by the power given to her by the ring she bears, she destroys the foundations of Dul-Guldur in Mirkwood. In other words, she tears down a mighty fortress by herself. Again, such offensive power as is scarcely displayed anywhere else.