Because there is still constant fighting happening internally in those places. Trials of position, trials of grievance, trials of refusal, trials of possession. All of these things happen frequently and regularly even in a Clan society that is "at peace" by relative description. This is what I mean when I say a Clan not fighting someone else is fighting itself. When elements Clan society experienced genuine peace in the inter-bellum Republic, it resulted in those patches of the Republic crumbling instantly to pursue conflict as soon as the opportunity presented itself. A matter of days.
This is not a suggestion of a particular occurrence in the fiction (though the Republic is a decent example), it is an observation of the nature of Clan society. The Warriors must War, whether on themselves or others, or the cracks form.
This is also BattleTech, so it's important to remember that "the state of not being at war" is not peace in the vast majority of occurrences.
I feel like Tamar Rising makes a pretty subtle but nonetheless cutting commentary on this point: the planets in the former Jade Falcon Occupation Zone that don't have warriors on them are marked with no colors. There may be Clan society in those systems sure, but there is not Clan society in those systems.
Trials are logical component of militaristic meritocracy, if military acumen is the benchmark by which politicians climb the ladder in a society then appropriate process is necessary which is precisely what trials are (and it's not like they do them in the middle of the crowded street at random just for laughs)
And trials also act as safety barrier against unchecked warfare, internal or otherwise
It's little different than arranged political marriages and political assassinations among planetary dukes in order to see who will be running a planet(s) and for how many generations, difference is that Clans have streamlined the process, removed PR spin and achieved much higher average turnover rate
Problems that Clans experienced in Stone's Republic are failure of the Republic not Clans but it was hardly the only problem that particular failed state had
As for structure of Clan societies and Jade Falcon example we should keep in mind two things:
1) All Clans are vastly different to one another, different Clans have as much in common as Capellans and Lyrans do AKA superficial similarities
2) Mongol Jade Falcons were anything but regular or even weird Clan and Malvina Hazen would be giving Lincoln Osis heebie jeebies, using them as some kind of example of average Clan makes as much sense as using Amaris' Rim Worlds Republic or Liao's Capelan Confederation as example of average Inner Sphere state
Mongol Falcons under Malvina Hazen failed and crumbled but that doesn't change the fact that more competent Clan societies have survived and thrived under various different (and often more difficult) circumstances and did it in many different ways
As for color of the map it's no different than if Coordinator and entire DCMS suddenly packed up and left Draconis Combine, for a while it would definitely drain the color from the part of the map where Combine used to be