I want to make status immunities common on equipment, which wouldn't work so well with tight coupling among skills in a skillset as you describe.
The answer to this is really the answer to the rest of your post: Skewed cycles. How common or not common different protections are matters less than how many protections can be stacked at once. Absorb (as well as Half and Null) can interfere with the DPS of a unit focused on elemental attacks, but you mitigate this by skewing how they're distributed so you can't Absorb/Null every element in the skillset at once. That both stops the unit from being made irrelevant without needing to invest extra skills for non-elemental damage and makes players who want to build teams around Absorb mechanics have to make meaningful decisions on which abilities heal them - assuming those abilities actually have unique properties and aren't merely palette-swaps of each other.
Status works the same way, what I described only really has issues working if you can block the entire skillset at once. This is why, if we assume an 8-skill skillset, it's best to have two different (but similar) core Skill Cycles that can function independently, alongside one or two supplementary abilities that compliment the core objectives of both. Even if parts of both core Skill Cycles are blocked, the remaining skills should still be able to be cobbled together in such a way that they result in a cohesive strategy, following such an outline.
Like everything, there's exceptions - eg, a Priest-type class may only have one core Skill Cycle and a few extra utility skills, a Monk-like class may forego strict Cycles for generalized offense that try to draw the opponent into a specific situation then choose the correct damage method based on the map layout of units around it, etc. And, while my example focused on utilizing negative statuses for a specific gameplay objective, there's nothing stopping using the other tools available to produce similar results - destruction or boosting of PA / MA / SP / CT / Br / Fa, destruction of gear, applying ally buffs and removing enemy buffs, etc. The point is to know where your unit is going and focus the core of their skillsets around that objective as the bedrock of their ability list, and let the complimentary widgets fall from that baseline.
Raven, what's your opinion on improving synergy between skillsets and equipment?
And, more specifically about this, there's plenty of simple things you can do with this based on how things are distributed. Eg, if you have a mod where Ice Element is often paired with a status infliction - ie, Slow - your Ice Absorb also blocking Slow helps build synergy with the player building up Absorb-based teams. There really isn't a detailed answer to this question without a more specific context, though, as equipment is ultimately beholden to the skills being used by the units that equip them, and how prevalent different aspects of the game are in those skills. (In this regard, you can count viable mid-late game weapons as also being abilities in terms of Element and Status, as they change the properties of the Attack Command A-Ability.)
The one general advice I can give though is that, aside from finding what trends you've built into the game and trying to complement them via equipment effects in one way or another, don't be afraid to let the items be simple. How simple they get away with being, again, depends on the specific context, but it's perfectly fine for an item to do exactly what it needs to do and nothing more. A complex item can be cool sometimes (as a rare item, for example), but how complex items are in their defensive properties in particular should be proportional to how ubiquitous what they're defending is. If most skillsets can drop liberal negative statuses, then yes, having status protection on gear be common is good to prevent the game devolving into constantly feeling the need to heal bad status off your units. But if your statuses are distributed stringently, the defenses to them should be equally so, etc.
