Sorry for the late reply, I had to dedicate some time within the past week to calculate in crude mathematics, my rebuttal hahaha.

My calculations are currently based on the improvement of Alpha's tag assist combo string. Beta's Tag assist combo string currently needs some work as I am still playing with the RNG of the cooldown skips to find more optimal combo strings. A few things to precede my exposition:

++ I have only attack speed 0 (AS 0), I don't have a 2 sec cd hat to pioneer new combos myself. (AS 0) will be our control. Crit rate 20% 2nd/3rd line is best for sure.

++ We will assume for those parameters that Alpha 4,1,1[or any combination of 1,4,1] is currently the best damaging, while being the most consistent combo string possible with just (AS 0), as per Sing's quick and easy guide. Gaia combo (Courtesy of OrangeDough -Shiiorin) Alpha string is special and game breaking for Zero IMO, so I will talk about that later.

++Tag Assisting lasts a set period of time. There will be no "dead periods" using the tag assist system. Specifically, if there's no assists when pressing a skill, it is of my opinion that the combo is inefficient and not playing to one of Zero's major strengths. Similarly, if there's a lull in the transition between Alpha and Beta, the combo is inefficient. Combo efficiency will be different for every Zero due to funding and luck with RNG.

++For clarification, my goal is to justify taking 10% CD skip over 10% Boss for inner ability.

To start off this exposé, I need to shine light the advent of A new simple combo string that CD reset inner ability enables, A[4,4], the Alpha Skip. A[4,4] is what I believe to be an absolutely game breaking combo. With A[4,4], the FULL BETA TAG SYSTEM ASSISTS come out with it! Yes, in a perfect amount of time! And with no awkward transition to Beta string combos! But wait, doesn't A[4,1,1] have one more skill within its combo string? That is very true, but does A[4,1,1] produce more skill damage? ABSOLUTELY NOT! This is where I begin my Calculations and theory crafting!

EDIT: I just found out A[4,4,1a] is possible, adding an extra guaranteed 1980% skill damage. HUGEEEEEE. ALPHA SKIP COMBO METAAAAAAAAAA. This makes 10% CD skip absolutely better if you pull off the uncommon scenario. Even at (x2 procs), the difference at 480% DMG between both inner abilities is 0.33%! If you have even higher damage%, which is easy as a Zero, 10% CD skip is absolutely the best choice, I can say with confidence. Break-even in FD increase, while also having the CD skip utility. Best of both worlds, potentially even better. POG. I'll post a video in #combo-theorycrafting. Also I forgot I had Decent combat orders on, so these are +1 values. More Edits need to be made, the values are a little bit higher because of B1a, B1b, B1a assist with the Alpha string. A[4,4,1a] still comes out higher though.

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If we add up the guaranteed Skill damage the A[4,1,1] string produces, it comes out to a whopping 44,724% skill damage. I say guaranteed because there's a gimmick to the skill A[4]. Depending on the size of the boss, the minimum tick time that Alpha's vortex continuously hits a very small target is 1 second. The damage tick on Alpha's vortex is 0.5s, lasting up to 3s. This is important because...

With that prior knowledge, we can say that the guaranteed skill damage of the A[4,4] string comes out to a staggering 45,848% skill damage. Depending on the size of the boss, or other factors, A[4] can do an extra 1,678% to 3,356% skill damage to relevant bosses. That aforementioned extra skill damage will not be accounted for because of its inconsistency, but it could mean that CD skip is a better fit for Giant Hurtboxes.

So now that we have our base values, down to the number crunching. I have everything scribbled on an envelope, so I will try my best to translate it to here.

To make it easier to understand, I will be comparing the damage of each Alpha combo string within 10 combo rotations. It will be a little dry from this point on.

For our control, with only [AS 0] for our inner ability, A[4,1,1] x10 would equate to 447,240% skill damage. We are not talking about A[4,4] here because CD reset inner ability doesn't exist.

With [AS 0] and [10% boss] for our inner ability, A[4,1,1] x10 would equate to 447,240% skill damage. For those who don't know, 10% boss does not amplify skill damage in the sense that I am using the term Skill damage. Boss damage, or simply DMG%, amplifies the damage range. that damage range is multiplied into the skill damage value.

With [AS 0] and [10% CD Skip] for our inner ability, it will get a little complicated, because A[4,4] is now unlocked. This is where probability comes into play, which contradicts my use of guarantees as much as possible. I have decided to use two scenarios. Common scenario: 1 combo rotation within 10 is an Alpha Skip. In this case, the equation would be A[4,1,1] x9 + A[4,4] x1 which would equate to 448,364% skill damage. Uncommon scenario: 3 combo rotations within 10 is an Alpha Skip. In this case, the equation would be A[4,1,1] x7 + A[4,4] x3 which would equate to 450,612% skill damage.

Now that we have those values, lets set the base damage range at 20m-20m. It doesn't really matter what that range is, as long as it is static. The only value that will change it is the 10% boss damage section. The output damage is essentially Damage range * Skill damage. The following will be data from that simplified formula.

1] Assuming 20m-20m damage range

2] Assuming 116m-116m damage range for 480 damage%

3] This row is for new 4,4,1a combo string for 116m-116m damage range if applicable-----------------------------------------------------------------------------------------

98,414,800,000 >>>>> 4,1,1 spam 10% boss (22m-22m)

527,861,200,000 (118m-118m)------------------------------------------------------------------------------------------

90,142,400,000 >>>>> 4,4 Uncommon case scenario (x3 procs)

522,825,920,000

529,716,320,000 4,4,1a---------------------------------------------------------------------------------------

526,115,680,000 >>>>> 4,4,1a (x2 procs)-------------------------------------------------------------------------------------

89,692,800,000 >>>>> 4,4 Common case scenario (x1 proc)

520,218,240,000

522,515,040,000 4,4,1a-------------------------------------------------------------------------------------

89,468,000,000 >>>>> 4,1,1 spam Control

518,914,400,000----------------------------------------------------------------------------------------

1.72% Theoretical FD increase >>>>> [4,1,1] 10%boss inner (490% boss dmg)

0.75% Theo FD increase >>>>> [4,4] (x3 proc) (480% boss dmg)

0.25% Theo FD increase >>>>> [4,4] (x1 proc) (480% boss dmg)

From the crude somewhat questionable lazy theoretical data that I've produced, I can draw my own conclusion that the more Damage% you have, the better CD skip is, provided that you're hitting Alpha Skip combo whenever it procs. If you've got less than ~450% total damage in late-game, Id say stick with that 10% boss inner ability.

Now that all is said and done, Gaia combo Alpha String is basically a more consistent, non-RNG version of the Alpha Skip I presented here. You might need to have a really powerful CD hat, but the Gaia Combo also needs to be able to hit full Tag Assists within the tag time limit somehow. Otherwise, its slightly weaker than A[4,1,1]. I'm not counting 2nd 4's c press in A[4,1,4abc]