Royalistflyer,
I'm confused
I'm sure I've missed something there, but you seem to have answered your own question. If your premis is
If you see first, you can shoot first, that is the point of stealth - to stop the bad guys seeing you first, if at all. If stealth achieves that, then yes it is worth it. Even if the enemy has a bigger stick it's no use to him if he can't use it.
As for close combat, you are right that it isn't a place you ever want to be in a real shooting war, even if your aircraft is really good at manoeuvring. You may win the close fight, but while you're doing it you are very vulnerable to his mates and so you want to kill the enemy at range or run away before it's too late.
That said, you may not always be able to avoid the merge and if that happens you better be able to fight WVR (and have weapons left). Clearly if you have good HOBS and enough weapons, manoeuvre isn't everything, but its importance does not go away. At that stage, stealth becomes less significant, but again its importance does not go away. All the above is what makes F-22 (for example) so effective - good stealth, good manoeuvrability and plenty of weapons.
As I have said many times before, the same agility (turn, accel and altitude) is also important pre-merge both for chucking your spears further and for making the other guy's work harder.
If your point is that good enemy sensors could defeat your stealth then, yes, you are exactly right. But he needs to have an effective way of doing that, which may rely on external systems and, therefore, significantly complicate his situation and create other vulnerabilities to attack.