MGS is a stealth game. Sure, you could beat them by run and gun, but it was much harder. Go beat MGS by just running around shooting every guy you see. It is a lot harder than MGS4, where it is almost encouraged. MGS4 made it so easy to just shoot your way through everything.
Also, Metal Gear started as a stealth action game. And I will continue to judge it on those merits and MGS4 gets an F.
I HAVE beaten it in both shooting and sneaking. I have beaten MGS1, MGS3, MGS4 both run and gun and no caution/no alert on Big Boss difficulty. I only beat MGS2 "normally" because I didn't like it much. Also beaten Peace Walker.
Shooting is EASY in EVERY MGS game because the enemy always pause when they discover you, meaning an easy headshot. MGS1 was a bit special because the clunkier controls made it harder to make accurate shots.
In MGS3, the enemy will quickly run out of soldiers, meaning that you can just run through the level after shooting all of them, and with 1st person view, very easy to get headshots. The ONLY thing that made the run and gun playthough harder was that the Sorrow is harder because of more soldier ghosts.
In MGS4, running and gunning has massive disadvantages to the other MGS's. They give you more guns and stuff to work, but unlike the other MGS's, there are bad things that happen with the run and gun strategy. Snake will throw up in the middle of combat if he shoots too many people. His psyche goes to 100% more or less instantly in a open firefight, and he won't be able aim for shit and his combat effectiveness drops extremely fast. These things didn't exist in previous games.
Also, in all games, you die pretty damn fast to bullets on Big Boss, so taking hits isn't usually an option.