A Draft Lottery For The NFL? Is It High Time?

Another thing I thought about with the recent idea of the Steelers going into the tank to improve their draft position: would it make sense to simply have all the non-playoff qualifiers simply be put into a draft lottery similar to, but not the same as, the one that has been used by the NBA?
Granted, the Steelers losing to move up a mere few spots wouldn't be the primary impetus for such an idea, since they'd probably draft in the high to mid teens anyway, at best. Of course, the Steelers would get a crack at the top of the draft, albeit a small one.
But think back to last year in the case of the Colts. Prior to last year, the Colts were a perennial playoff team. All of a sudden... KABOOM... on the clock at the end of the season! Then, this year, back to the playoffs with guns-a-blazin' (helped with that fourth place schedule as well, no doubt).
The idea I had would involve the 20 teams who don't get to go to the playoffs being in a lottery to determine the top five in the draft order, with no team having more than a single selection in the top five. Each team would have as many chances to get in as their position in the draft order would allow in descending order, with the least teams getting the most chances.
If a team, somehow, has more than one selection, since picks are routinely traded for future considerations, the selection which is of higher value would be combined with the selection of lower value and the average would determine how many chances that team had to get into the top five. For example: say a team has the sixth position via a trade AND their own position at 16. Since that would average out to 11, the team would get the same number of chances as the team in the 11th position. No team would get more than one chance to become one of the top five teams.
The teams who do not secure a spot in the top five would draft in the same traditional fashion as always from 6 to 20, with the team with the worst record drafting highest.
I feel like this would be a more equitable solution to teams going in the tank to secure a more favorable draft slot. It's not to say that the teams that wouldn't succeed wouldn't still go into the tank to secure more chances. However, if that was the worst case, perhaps every draft position could be subject to lottery positioning to insure that all teams play hard in all games to prevent such a scenario from materializing.
Just a trial balloon to see what others are thinking.
In the spirit of that: thoughts?...