1) No, because private matches, and then picking up a pug means technically a public match now, so even making Piravte an exception....
2) No, because level =/= skill, a Gold/Plat level player has no reason to want to pug Bronze where they would be bored because it is just a competition to floor-wipe the enemies before the other guy does, and also not die.
3) No, because sometimes the main thing for a build is just... guns. Or the one skill. Like a volus with shield boost can fufill its role well enough. A Destroyer with some devastator can still shoot things. A batarian can still punch things. Sure, they're not as effective as they could be, but its not like they're an elcor armed with only a stick of taffy - the difference is ultimately down the skill and handling.
This is like requiring an N7 of 1200 (not 120, 1200) to join a Gold lobby. NUMBERS. The numbers may be related, but not always. Usually not.
If someone has low-level and an N7 higher than, what, four? That means they've played this game a few times before. Promotion. Whatever. They know how to shoot their gun.