Basics: with less influence than all shapers save for Professor (who ignores influence as his ability, so....) you are taking Kit for her ability and only her ability.

Pros:

No matter who you look at, of any and all other runners, with a single breaker and a a few credits Kit is still the safest face check in the game. To Kit with 3 cards, 3 credits, and a Gordian Blade A Komainu is as as dangerous as an Errand Boy or a Bastion. All are a 3 break if they are the ICE you are running blindly into.

Literally, if your first turn is a Sure Gamble, a Cyber-Cypher, and a The Maker's Eye you can run R&D on the first turn and know you will get in, unless the corp has ICE stacked two deep or more than 10 credits or they have Wraparound in the opening hand. And for most ice, it costs as many credits to break as the ice has subroutines.

Go to Sneakdoor Zeta for an example and you'll see using Rainbow and Chimera as examples that Decoders are often cheaper overall than Sentries as breaking. Late game, this can simply be a way to make sure you have cheap breaks.

And a dozen more ways to say, you can get by cheaper safer runs with Kit than with any other runner.

Cons:

So why isn't she more dominant? 10 influence is a killer for sure. Want to run Spooned to be able to destroy that major piece of ice? Well it's close to 1/3 of your influence right there. You have to make hard choices.

Code gates often want to sit on the outside anyway? Chum... Inazuma... even Builder and RSVP... You don't want all code gates out front, but many of them work well at the outermost ice in a server. And so your ability is a little moot.

The ability only works on the first ice you encounter on the first run you make in a turn. On your second run, you are just a easy a victim as Kate "Mac" McCaffrey: Digital Tinker, only you didn't get the link, the econ ability, or the extra 5 influence.

Wraparound still works just as well as it does against AI breakers (although Swordsman is a joke).

Mitigating the Cons

Make a deck that only intends to run once a turn. Perhaps you can spend all the clicks on Magnum Opus or simply plan to use Lockpick for all your econ knowing you let the Rig do most of your work.

Use all your shaper tutor power to simply make sure you always know the tool you need. Maybe they had to run get a Chum to feel safe? Fine, but by then you still knew what was behind the chum and had the time to go get the breaker for that.

Potential traps

Paintbrush is really click intense and means you need to be a big rig builder even if you can trust in having some easy code gate power. Unless you are sure you can trust the corp to

Spooned sounds like a good idea, except that you almost would rather break the non-code gates since those are the trouble ones one they aren't the first ice in a turn.

ZU.13 Key Master is usually a great cheap breaker for aggressive running. But it's the wrong way to go here. If you plan to run more than a few times in the whole game, splurge dude! It's not like you are Exile and need something you can pitch when every you want. Perhaps you skimp on a killer or a fracter, but this is going to be your big boy. Make it something you know you will use and use and use.

Pros? If they don't run it that very first time, you make back the rez cost. Two Rounds of not running it? Profit. If they do run it right away, it costs them 2 to trash. Basically unless they have a deck based on rewarding successful runs (Desperado, John Masanori. etc) if they don't run it first the runner turn after you install it, you are breaking even at bare worst. Remember, a trash cost isn't just a way to keep the runner from getting rid of your card. It is also a way to make the runner broke so you can get a scoring window.

Cons... As popular as Desperado and builds using it's strategy are unless you do something to keep this safe, it's costing you more than the runner. Also, Gravedigger mill deck has become a thing. All in all this is an easy way to get a card into the archives to allow you to get another card into the archives if the runner wants you milled.

So what do you do to make sure this isn't a break-even card? If you know your opponent will run it anyway, you could put a small taxing ice on it, like Pop-up Window. Mostly that's just going to mean you break even instead of you falling behind the runner. (*see below for the math, if you aren't sure.) Instead use Jenteki IDs that will help. Jinteki: Replicating Perfection says that they have to hit part of your taxing centrals and then run the moneymaker. It costs you the and it costs them breaking the subroutines on Komainu or even just paying Pup one more time to get into your empty archives before they can trash this and best of all you get your rez cost back guarunteed. Or try Industrial Genomics: Growing Solutions to make trashing it more painful. Add in Hostile Takeover, Turtlebacks, and Encryption Protocol to make just installing it that much more of a gain for you or a loss for them. You might get a few turns of use just because it isn't worth the net damage or the fistful of to trash.

*(install, 2 rez, lose 1 installing Pop-up Window, gain 1 when he runs it = 2, run, runner loses 1 from Pop-up Window, but gains 1 from Desperado = same as if both runner and corp lost 1 and 2, while corp for 1 until you use the server again or unless the runner gains something else from the run... to close to call really, right?)

Pros

Potentially the best card draw to fill back up after a damaging run or to prepare for a turn when you expect a counterstrike.

Cons

Only useful compared to "click to draw a card" if you are drawing 3 cards or more, but if you are only getting three cards, you might as well use a Diesel.
High influence compared to Quality Time and even Diesel

Thoughts

Fluff is a bit of a turn off for some.
Unlike Quality  Time or Diesel this card does not work well for the start of a turn when you want to be drawing to have as many options as you can manage.
Clearly in the Data Pack with Hayley Kaplan and  Comet for a reason as they will need lots of card draw to run smoothly.
Still not enough to make starlight funding crusade change status from "Mistake" to "Situational at best."