The system you're talking about sounds like a weak variation of what is called "best roster" rules...and it's used in a number of contests, including Footballguys.com. It takes your entire roster, there are no starters or bench, and it counts the highest scoring QB, 2x RBs, 2x WRs, TE, K and D.
I did one of those once. Most of the guys in the group loved the draft, but were too busy/lazy/disinterested in setting rosters, trades etc during the season. So we had the draft, checked our scores every week and that was it.
Another variation that I know some software allows, but extremely few leagues ever make use of (and none that I have ever been in) allows you to draft a unit. So rather than drafting Tom Brady you draft the NE QB. Another variation allows you to get points for a team category, eg, you get points for how many yards of passing yards the Dolphins have regardless if thrown by the starting QB, backup QB or a RB on a trick play. The software allows all kinds of variations, it is just folks like the OP that would want such rules are extremely rare.