Is there a disadvantage to being higher level in low trophy arenas?

Solution 1:

Your level only affects the HP and damage of your towers. There is no other effect of your level.

As you can see, there isn't any disadvantage to having a high level. This applies to all arenas.

It may also have a demoralizing effect on your opponent, if they're level or two lower. (Less on later on where levels even out and people realize that the cards and strategies play much larger role than a 100 or so more HP on the tower.)