Are there any negatives to gaining levels? i.e. enemies will be stronger strictly based on what level your character is.
Enemies don't scale level wise but they do in number. As in if you the max level you will be fighting much bigger armies then if you were level 5.
No, there are no negatives at all to gaining levels. In fact, there are only positives as your training skill only affects units that are lower level than you. Enemies in the game are all fixed level wise and do not scale.
Yes, it does has a negative because bandit lairs that usually have 20 bandits eventually have around 75. I had to fight 100 in a single fight and won with 5 health left and 5 wounded.
As of this post I'm level 34 (playing on PS4), and I have NOT noticed any overly strong correlation between enemy army size or quality level and player level ... it there is one, it's modest at best.
My biggest problem is boredom ... level progression slows to a crawl above 30, and after a while all battles seem the same, and XP rewards seem chintzy.