Shunsui never truly intended to use Bankai, and him stating he would was because of Ukitake. The context of that scene makes it clear that he was only trying to keep Ukitake from joining in the battle with him, as Ukitake gave the reason he was intervening as being because Shunsui wasn't going to use Bankai (which was the first mention of Bankai), and after Shunsu jokingly says he was just about to, Ukitake finds another reason (That Starrk/Lily is technically 2 on 1 and his abilities are better suited) and tells Shunsui not to complain
As for Shunsui's games, I can see Ichigo figuring them out. He's been shown repeatedly to be incredibly perpective, infact Gin even called it scary, so while it's unfair to say he'd figure it out exactly as Starrk did, it's also unfair to assume he wouldn't. The only game that really requires figuring out is Iro Oni, as Kageoni would be rendered completely ineffective if the fight takes place in the air
Were this Pre-Skip Ichigo I'd go with Shun, but the Tournament version of Ichigo here takes the win for me
All Ichigo has is raw power. It isn't enough to take down a cunning opponent like Kyoraku.
I wouldn't say everything ichigo has is just raw power. He does have that but its not like he aims to (or actually does) fight stupidly.
Ichigo's bankai is without a doubt the most convenient one we have seen in the manga. If anything it is basically the most hax one we have seen. From his bankai ichigo gets a boost to virtually every form of shinigami combat available to shinigami. He gets significantly enhanced offense, he gets significantly enhanced speed and a more powerful long range attack. The enhanced sword and speed he has overall makes a perfect boost for his defense as well. His shunpo works perfectly well with his enhanced speed. No other shinigami gets so perfectly balanced skills from his sword. Some get insane offense (komamura/ikkaku), some get range (soifon) and some even get batshit crazy hax stuff (yamamoto) but none of them covers so many areas of combat at the level of bankai. Yamamoto had insane range, offense and defense but his bankai did not cover any aspect of speed whatsoever. Komamura has offense and perhaps some defense but no other aspect gets enhanced.... Soifon is just a nuke. Ichigo has a bankai which enhances every possible aspect of combat to the level of bankai basically. So how is that relevant against shunsui?
Shunsui's shikai in particular does not offer increase speed, stamina, offense or defense. It merely changes the rules of battle. At most his offense relies on the rules of the game but other than that he does not get enhanced defense. His only real advantage during the games is the fact that he knows the rules. Other than that the games are as inconvenient to him as they are to his enemy.
So how does shunsui's shikai match up against ichigo's bankai? I would make the point that ichigo's bankai is the closest thing you can get to a cheat code in the games (safe for aizen's KS). In particular speed is an issue. A factor of the games is that they generally allow you to cut places and do damage based on the rules. However where someone is cut is also a factor. Cutting the jugular won't be the same as cutting the stomach. So you have ichigo with his bankai which would allow him to a great extent to be cut at places of minimal damage altogether and more easily aim for more damaging places himself. The manga has not yet been too specific as to exactly how fast ichigo is right now but it does seem like he is a decent bit faster than what he used to be with a mask in which case shunsui should be wary IMO.
A big part of the issue here is that shunsui does not have bankai. I would argue that without bankai fighting a captain level fighting with bankai would invariably put him at a disadvantage. Shunsui is a capable fighter but I can't imagine him overcoming ichigo with just shikai when ichigo has so much stuff going for him now.
Its not like ichigo fights stupidly and shunsui makes a point of fighting smart. Shunsui needs to fight like he does because his games are as much of a risk to him as to his enemy. Ichigo fights the way he does because his abilities are in themselves quite straightforward.