Never quite felt like that to me. Sephiroth's madness stemmed from the fact he knew he was different, just not how or why, and learning those truths drove him off the deep end. He's considerably more sane in the main narrative of VII, just with... y'know, the whole "genocide" thing going on. In Crisis Core and such he has good friends in Angel and Genesis, and later Zack, Shinra's full support, and even a fanclub. It's the loss of Angeal and Genesis pushing him towards the ugly truth that pushes him into madness. Pressure may have been there, but it wasn't until those events that he lost it.
The Warrior of Light, conversely, hides their pain behind the mask (persona) of the same name. Strip that away and you get "Fray" - a ruthless, cold-hearted vigilante who does favors for people only if they think they'll get a good scrap out of it, and is also a PTSD riddled mess. You acknowledge that side of you without letting it control you, but it's still there.
For fun, try changing some of "Fray"'s dialogue to first person. It gets heartbreaking very, very quickly.
Hah hah...“surrender your weapon?" After what happened in Ul'dah? They must be mad. Pay attention, [Forename]. This could be the greatest moment of my life... That is, if I could stop denying the truth that's been staring me in the face since the moment we met. Say my name. Say it. My real name. Our real name! Come now, I knew Fray was dead from the beginning, but I didn't care! I had a sword and a soul crystal. But what I wanted was a mentor. A mentor with the gifts and the knowledge. A dark knight who could guide me on the path─who I could aspire to become. A [wo]man who was free to say and do the things I would not. ...Even now, I continue to deny it. Well. Deny yourself all you want. You cannot deny what I have done. Have I not been good to you? Have I not given you everything I promised? Did I not help you to hear the whispers of your very soul!? Open your eyes. Look. Do you see now? Do you see?
...
They have borne witness to the darkness within me... To what lies beneath the mask...
...
A fantastic display of willful ignorance... Wipe the slate clean. Forgive and forget! Convince yourselves that I can be controlled... The Warrior of Light! Your Weapon of Light!