CitM, you'd get a better reaction if your tone wasn't so combative, but then again this is Dumpshock, so... meh.
But Falconer and Shinobi... the rules, the literal words that are on the page, are clear and do not say what you think they say.
One:
QUOTE (SR5, page 129, second column, under the heading Skill Ratings)
The skill Rating is a numerical value ranging from 1, representing the most rudimentary skill, to 12 (or 13 with the Aptitude quality)
If there exists any exception to this rule for player characters, please cite your page number and where exactly you found it. Please note Dracoforms are NPCs, and as such are not subject to this rule. It applies during character creation, it applies after character creation, it applies if you choose Improved Ability, it applies if you don't choose Improved Ability. Hell, it even applies if I spread peanut butter on my eyes and do the funky chicken,
even though it never says it applies if I spread peanut butter on my eyes and do the funky chicken. This is because you need an affirmative exception to this rule in order to qualify as an exception. If it doesn't specifically say it doesn't apply, it applies.
Two:
QUOTE (SR5, page 309, second column, under the heading Improved Ability)
This power increases the Rating of a specific Combat, Physical, Social, Technical, or Vehicle skill per level of the power.
Please note it says "increases the Rating." If the skill was a 4, buying one level in Improved Ability means the skill is now at a rating of 5, not 4+1. If it was 4+1, the power would state that for each level of the power, it would increase the dice pool when using the specific skill by the level of the power. It doesn't, it directly modifies the Rating of the skill. If it created a "modified skill rating" like it did in SR4, it would specifically state that, but it's not even like the power was copy/pasted from the previous edition without any thought. There was a conscious decision to change the power as written from the previous edition and include the specific rule that showed up.
The limit in Improved Ability is a limit for the levels you can take for that specific power, not on the rating of the skill. The levels of the power are not equivilent to the rating of the skill and as such are two different things with two different rules limiting their acquisition. Additionally, you still have the above limit on all skill ratings that applies
at the same time as the limit on the levels you can take of Improved Ability. You can have bought a skill of 10 and two levels of improved ability, or you can have two levels in the skill and, because the limit on the power is recursive, you can have 10 levels in improved ability. But under no circumstances can you have a skill of 10 and 5 levels of improved ability or a skill of 5 and 10 levels of improved ability, because that would make the
rating of the skill itself a 15. Which is over the rule on page 129 and there is nothing that says that limit ever goes away under any circumstance.
Is this intended? Probably not. Does that matter? Not in the slightest. Until such time as either CGL or Missions (which is the only time RAW actually matters) puts forth an errata, this is RAW. If you want to change it for your personal table to work like you obviously want it to work,
do it. I personally am going to use it as a dice pool modifier and not a direct modification of the skill rating itself, but I'm also not going to attempt to say that the words on the page say something other than what they say.
Further, to address the "Gods out of the Gate" situation:
QUOTE (SR5, page 88, first column, under the heading What the Numbers Mean)
The first number in the skills column is the number of skill points a character has to spend on individual skills. These skill points are generally used to purchase Active skills, though they can be used for Knowledge and Language skills too (see below). If you don’t get exactly the skill ratings you want in this step, remember that skills may also be raised with Karma at the end of character creation. In this step, it only takes one skill priority point to either acquire a new skill or raise a skill rating by 1.
This establishes that spending skill points in character creation specifically increases the skill rating equal to the points spent on the skill, which, if your remember from above, is also what Improved Ability does. And moving further on that same page, skipping the skill group rules, gets us to:
QUOTE (SR5, page 88, second column, under the heading What the Numbers Mean)
In character generation, the highest characters can raise a skill is 6 (7 if they purchase the Aptitude quality). After character generation, the highest rating a skill can hit is 12 (13 with the Aptitude quality).
In addition to once again reiterating that the skill cap is 12/13 at all times after character generation, during character creation you are limited to a skill of 6. Which according to the above paragraph, means a skill rating of 6.
In character creation, you cannot exceed a skill rating of 6 and it doesn't matter how you get to a skill rating of 6. If you spend 6 skill points and then buy even a single level of Improved Ability during character creation (not counting a focus), means that the skill is now above the skill rating limit in character creation (without the Aptitude quality) as Improved Ability
directly modifies the skill rating itself, and does not either create a bonus to the roll, or as in SR4, create a 'modified skill rating'.
Post character creation, a player can take any skill at 2 or higher directly to the cap of 12/13 due to how the limit on Improved Ability is recursively worded, but during character creation you are limited to a skill rating of 6, no matter if you get there through skill points or the Improved Ability power (or for that matter, the Reflex Recorder). Whether you chose to use these rules or not, these are the Rules As Written, and if you choose not to use the Rules As Written, that is by definition, a house rule. Which, again,
is totally fine. But disagreeing with what the literal words on the page say doesn't change what is actually written on that page.