Purposes of maintainig level 7 ?

[Ultima Shadow]

I think there is a No Junction challenge or something?

While the "No Junction" challenge probably is the hardest, it's also kinda boring because of the very limited options in battle.
The challenge I personally prefere is therefore "No stat-junction", as in: allow "commands" such as "Draw", "Magic", "Item" etc to be junctioned, but nothing else. To add a bit more challenge to that, you can also stick with everyone's first weapons and never upgrade.

...and it's actually harder if you keep a normal level than if you stick to low levels.