First I have absolutely zero idea what you are talking about with cheese and cooldowns. If you are hiding somewhere not attacking because you are waiting for your cooldowns to end, YOU ARE NOT CONTRIBUTING TO THE FIGHT. You are leaving your team down a person, making success less likely.
Everything I have written is for 100% solo in mind. As it stands, this first Act with a party of 4 is a complete steamroll. I think a monkey could randomly roll all 4 characters and you'd still beat the Act. I can't say anything about the rest of the game because it's not there.
Sounds to me like you've founds some kind of edge case where someone can be boring and exploit a game at the cost of making it completely unfun for THEMSELVES. Whoop-de-do. That, to me, does not seem like it is a problem which needs fixing when the cost of fixing it means that using sneak or invisibility in a normal way is not allowed.
I'm not sure what you mean by edge case. What I have described you can do in literally every battle. You have inspired a different idea, which I will get to later.
Well, given that basic attacks cost 2 AP, Sneak costs 1 AP, you get 4 AP per turn and moving will cost you 1 AP or more to reach an enemy, That means a Rogue would need to start 5 or so meters nearby an enemy, outside of any sight lines, the enemy can not move and MAYBE the Rogue can move to just outside of the circle with 1 AP, Sneak with 1 AP, move into the circle with 0 AP (assuming there's a free fraction of a move left), and attack once, after which they are out of AP and will take a beating.
There is a difference between "not being able to enter sneak" and "breaking sneak".
You have now completely eliminated backstabbing from happening AT ALL except for Vault, which doesn't even require the Back-Stabber Talent.
This is absolutely true. Not a good idea.
It also does have the similar issue of the others in that if the enemy starts looking around for you, it means that you are essentially forbidden from sneaking at the end of your turn.
If you ARE a rogue, then at the very least you have Cloak and Dagger. That's 1AP to go anywhere. What's the problem? 2AP to attack 1AP to flee 1AP to sneak. In this case you can flee so far that if the AI looks for you chances are if you chose correctly you'll be able to stay in sneak.
Your ideas boil down to "I think Rogues should be completely useless. Delete Sneak and Invisibility from combat completely".
I'm not sure if your conclusion is correct. What I tried to illustrate is that if even in the WORST case where I am the least roguelike thing imaginable I can STILL sneak out then there's something wrong with that mechanic.
Here is a new idea, tell me what you think:
Cooldowns don't tick while in sneak/invis.
This way, boring (smart) people cannot exploit (use basic game mechanics that are there at your disposal) this mechanic.