I just think it makes tournaments absolutely trivial in late game, when you also have strong armour and the only thing that can kill you now is a Headshot by a javelin.
Make different Tournaments:
Regular tournament: As they are now in Cities and everybody gets a medium armour of the town culture whith more varied faction equipment as a reward
Royal tournaments: Hosted by nobles in Castles at special occasions, marriages or Peace Treaties for example. These would last a Week and be the gathering of high society and could include special Quests given by rivaling Nobles, like sabotaging the opponents gear or abducting their Rivals Daughter.
The player can convert Money into Renown and Influence this way if he were to host one himself (50 000 denars --) 10 Influence and 5 Renown per attending Noble and 50 if you were to win such a tournament ; Only Nobles and named Characters are allowed to attend, Stronger weapons and everybody gets to bring their own armour. With special tornament types like jousting or Archery Contests.
The player would need to pay a decent sum of money (5000 Denars?) and be at least clan tier 2-3 in order to attend and the reward can be a decorated piece of armour or masterwork weapons. This would also give opportunity to strenghten Relations with nobles of the Realm or make new enemies.