Heres how I think about gameover screens

Pros

  *  Game has a hardcore element to it, attractive to certain type of gamer.

  *  Game has more emotional investment to players due to high stakes.

  *  Easier to add more randomness in generation of levels, the player will have to play old levels over and you can change them.

Cons

  *  Massive turn off to a large amount of players

  *  Players are likely to rage after death, where they may have stayed engaged if they could restart on the level they died.

  *  People are likely to see less of your content.

So, it depends on if you are making purposely designed levels, probably no game overs is best, if there is variance in each run, MAYBE game overs are ok.

If I was in your shoes, I would have a "hardcore mode" with certain achievements for beating the game, and regular mode for 90% of players.

Hope this helps!  Good luck with your game mate!  :)