That's an idea but IMO our team will become totally unbalanced. Ideally in a 3 man midfield :
1. is the defensive screen whose main job is to guard the central defenders.
2. is the primary playmaker than can control the tempo of a game while in possession of the ball.
3. is a box-to box midfielder or has good dribbling ability/ mobility to extent plays.
If we look at some of the better traditional 4-3-3/ 4-3-1-2 teams of the past decade :
Gattuso 1, Pirlo 2, Seedorf 3
Busquets 1, Xavi 2, Iniesta 3.
Alonso 1/2 hybrid, Modric 2/3 hybrid, Di Maria 3.
Edmilson 1, Xavi 2, Deco 3.
If we replace the 2 with two #3s there's every chance to lose control of the game, especially vs possession oriented teams because even though Herrera and Strootman are technically gifted - neither those 2 or Blind have the vision or passing range to really impose themselves on the game. The sole example of a successful team using 2 box-to-box player in the central areas Juventus but they have Pirlo as the playmaker.
What we need more than anything else IMO is someone who is like a younger Xabi or Scholes in his older days when he just sat back and picked teams apart. A player like him surrounded by the energy, workrate and mobility of Herrera + Di Maria would be a deadly combination and instantly catapult the current lot into one of the best midfields in Europe. I think someone like Koke or Ruben Neves (very inexperienced) would be better suited to that role than Strootman because both have great vision and the requisite passing range/ defensive work-rate.
There isn't a fixed way to play the game, likewise, there isn't a fixed set of players to play a midfield three. A regista is an important player but he is not be all and end all. You do realise that Xavi, Modric and Pirlo are all very different players? At the end of it, it really depends on how the team is set up and what kind of players there are in the team. Most of the time, teams who wins the midfield battle have 1) More bodies in midfield and 2) Flexibility.
Juventus have Pirlo as their main playmaker but they don't play a genuine #10 whereas we have Rooney and Mata, a hybrid attacking midfielder/CM (Di Maria) and Herrara a mix between a #8 and a #10. If LVG manages to get his philosophy through, our 3-5-2 would have far more tactical flexibility compared to Juventus who sometimes find themselves in major trouble when a team sacrifices someone to man-mark Pirlo.
Barca's midfield trio fits your description of the "ideal" 3 man midfield, but it is incredibly fluid and have other players playing in such close proximity thus enabling them to have complete control over the ball. Xavi also played with two players who would easily make the top 10 all time list.
Pirlo at AC Milan played with sometimes not one but three playmakers. He strangely turned shit for awhile when they all left and he became the sole playmaker.
Alonso was great for Real, but got found out a few times in the big games, especially in the CL when Ozil and Ronaldo wasn't giving the midfield enough support. That's the reason why Mourinho went to buy Modric.