I was away for a few days so didn't follow the whole discussion and it's possible I've missed something but the problem here is we don't really have wingers who would do what you're talking about.
Yes, we can use Coutinho as LW but
1. He's used to move centrally often so you can't really expect him to stay on the wing and take on defenders the whole game like Neymar did to create more space for Messi/Suarez in the middle. Yes, Cou could and I don't doubt he would (try to) adapt if that's what EV would ask him to do but I don't think that's the case. I think EV deliberately doesn't want to play with a full-time LW because he wants to give more offensive freedom to Alba. With our interest in Griezmann (who again could be used as "false winger" but is more comfortable in the middle) instead of another true winger I don't think EV is planning to use a traditional 4-3-3 that you want even in the next season(s).
2. Cou can't play in CL so I don't see EV using one system in La Liga and other in CL.
With Dembele's injury problems our only wingers are Denis and Vidal who are both not good enough to be starters which we can probably agree on.
Do you think we'd do better with Coutinho-Messi-Vidal/Denis in 4-3-3 than Iniesta/Cou-Busi-Raki-Gomes/Paulinho; Messi-Suarez in 4-4-2? I don't. We should have the best players in the lineup and both Messi and Suarez are undoubtely among our best 11 players. (Gomes/Paulinho are not but I still think they give us more than Denis/Vidal - and that's coming from probably one of the biggest Vidal's supporters here). Valverde's job is to find the right balance and formation to use those 11 players and he's done that so far and I don't doubt he'll do it in the future again after he'll find out how to utilise both Coutinho and Dembele (though we most likely won't see much of him until next season) with the rest of the team.
Yes, Coutinho should definitely cut in. His purpose would be that of an inverted winger. That's his style and his best position in my opinion. Dembélé can take care of the RW. His ball losses were overblown in the Getafe game... He created chances and was dangerous both close to the box and when carrying the ball from deep. In fact both Coutinho and Dembélé were more dangerous than Suarez.
Anyway, I'm talking about balance here and I have been all along. People are getting caught up in this whole Dembélé/Coutinho thing when the bigger problem is the accommodation of both Messi and Suárez. This is and always has been the problem. I don't think there is anybody that disagrees on that... In order to get the best players on the field and maintain a balanced squad in terms of our bread and butter midfield one of Messi or Suarez has to sit out. To accommodate both with a 4-2-3-1 you end up leaving one of Iniesta or Coutinho out in a significantly weakened midfield and it's the same with the 4-4-2 that includes Coutinho/Iniesta and Dembele. In fact it ends up being a lopsided 4-2-3-1 in any event. Then we have the issue of Suárez touch and general play not being of sufficient quality for him to be a sole striker.
Why do you think the goals have dried up recently? Messi is too deep because their is no creativity in central midfield with a double pivot of Busquets and Rakitic and Suárez is just being Suárez with his allround play being below standard apart from the goals. In order to play a 4-2-3-1 a deep lying playmaker is needed. Show me one top team that plays a 4-2-3-1 without a deep lying playmaker...
I'd much rather Valverde go back to his workhorse 4-4-2 then. But then what was the point of spending all that money on 2 technical and creative players?
Of course EV is trying to find the best position for Coutinho but I don't think he's caught between different systems. I have total confidence he knows what he's doing. He can experiment with different lineups and players in trainings but you can only find out if and how some things you're working on in tranings will look in game situations. Sometimes they work, other times they don't. EV didn't have a preseason with Coutinho and Dembele so it's understandable he has to do that now in La Liga games. With our good lead he could afford that but I think he'll go back to the proven 4-4-2 against Chelsea, AM and in other important games.
This is not true. Valverde already knows Coutinho's best positions (he clearly doesn't see him as a CM) and that's why he is played wide on either flank. It's the same for Dembele... Valverde's problem is Messi and Suárez and fitting them into the same 11. The same problem Lucho had still exists and Valverde continues to faff around despite more than half the season already gone.
That comfortable lead you speak of has been reduced to something uncomfortable already with games against Valencia, Atleti and Madrid still to be played.
With players available our best bets are 4-3-3 or 4-4-2 with workhorses.