This is a direct quote from the Player’s Handbook: 

“Rogues rely on skill, stealth, and their foes’ vulnerabilities to get the upper hand in any situation. They have a knack for finding the solution to just about any problem, demonstrating a resourcefulness and versatility that is the cornerstone of any successful adventuring party.” 

No other class is praised in this way. I’ve been playing a Rogue for a while now, and I keep getting into sticky situations, but always make it out unscathed with a clever solution. Rogues are indeed the cornerstone of adventure parties, and even though my character isn’t the best at fighting or magic, my Charisma and Persuasion are ridiculously high. (Why don’t more Rogues specialize in Charisma? What’s better than a thief who is great at Persuasion?) Rogues are the ones that are greatest at exploring, and when it comes to combat, can hold their own. (I like to use Persuasion to make the enemy surrender after a few rounds, then pickpocket them.) 

If you disagree, then I just want to say that I am still on my quest to figure out which is the best class, no matter how you play them, and my opinion may change.

Why don't more rogues specialize in charisma?

Rogues need dex more that anything else. To be anywhere close to holding there own in combat they need sneek attack and that means a dex based weapon. Out of combat they are supposed to be the sneaky ones (stealth needs dex) even your quote says rogies rely on stealth.

The question then becomes what should a rogues secondary and tertiary stat be there are several candidates.

• Con: All characters  like more hit points especially if going into melee, they can disengage as a bonus action but moving in attacking and moving out means they are still quite close to the enemy. Con saves are also very common. For a melee rogue I woud probably but con second, I do however know a player with a ranged rogue that dumped con.
• Wis: Rogues need to be perceptive, if they are scouting ahead they need ot spot the traps or hear the hostiles before being heard by them.Wis saves are also common and a failure can be VERY bad. Wisdom would be my go to second stat for a ranged rogue and third for melee.
• Int: Rogues should be able to determine where the loot is hidden and that requires investigation, from a mechanical point of view rogues do not need to prioritise intelligence unless they are an arcane trickster who wants ot pick spells that require decent int. However many parties have no wizard or artificer and the rogue might be in the best position to get decent int for investigation and knowledge based rolls.
• Cha: If you get caught high persuasion / deception might mean you can talk your way out of it and for some styles of rogue this can be beneficial, some swashbuckler features also run off charisma, though the party face is usually best filled by a character that has charisma as their primary start (most parties I have been in have at least one of a warlock, sorcerer, bard or paladin.
• Str: Usually Little need for a rogue to  have a decent strength

You make very good points about the dexterity for rogues. My rogue isn’t really the typical rogue; he’s more of a trickster-showman who uses quick thinking to talk his way out of any situation. That being said, stealth and other dex abilities are also used a great deal. Kind of like a Loki-type dude. For example, he would rather trick an opponent (like a Druid being a spider, and telling an army of Drow that it’s Lolth, and while they’re distracted, I sneak attack them.) When I made him I disregarded con and definitely regret it; having to resort to cha to get out of situations. It all comes down to what kind of character you want your rogue to be.

If you play 5e you can get the best of both worlds - rogue 11, multiclass over to fighter and or ranger for more battle powers. After lv 11 the rogue doesnt really get much.

in the new edition this will change to lv 7 since you get reliable talent earlier. You wont be very good at combat though.

I agree with the OP, because I also tend to play rogues and getting into and out of trouble is always a specialty of rogues. Everyone focuses on damage potential, but most of the games I am in have the damage folks sewn up, but then we end up in a skill or social challenge and it is your time to shine with versatility. You can lie, convince, and intimidate your way through a social encounter equally well. You might need a few knowledge skills working in tandem, or just better versatility as the engagement shifts venues. A balanced game in my groups is usually 65% social/puzzle/clever play and 35% combat. A rogues job is to help set the others up for success and pick off weak opponents while the folks that focused on damage builds do their thing. I have spent quite a few battles ferrying potions with BA dashes, then popping off a random sneak attack.

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The odds.