I think Tryndamere's kit is very badly designed, offering almost no counterplay other than either "I am a champion who can kill him 1v1" or "I am a champion who will die if I go too near him".
He's "balanced" by his poor teamfighting ability and his huge vulnerability to CC, but he's not a well-designed or fun champion.
If you are a certain type of champion (generally a squishy with low mobility), then you can't fight him because he takes away all your attack damage, you can't run away from him because he can spin after you and is faster than you (plus, he can slow you if you try to run), and you can't kill him because he's unkillable and probably out-damages you.
On the flip side of the coin, if you are someone who is tanky enough to survive him, or has enough CC to disable him, or are just in a teamfight with allies who can CC him - he's completely useless.
His gameplay pattern is to basically just push a lane as much as he can, and if he gets piled on or attacked too much, to just spin away, ulting if necessary, then recall, buy some items, and come back and do it again.
Also, as you said, he plays very much like a "coward", running away from fights, only attacking if he can smash someone weak, and basically just using his ultimate to run away instead of using it to make a devastating last stand - not very barbarian hero-like behaviour.