The idea of the player with limited knowledge and control is as old as gaming. When you are playing against other Humans, as in Poker or the boardgame Diplomacy, limited control and knowledge is, in fact, the essence of the game.
I remember fondly the old SPI boardgame, Franco-Prussian War, which deliberately tried to give the player trhe same lack of information a 'real' general would have had: all combat factors and sizes of units were hidden, a bunch of 'dummy' units were on the map, so you did not know what you were facing, exactly, until Combat started - and sometimes not very certain even then. In a set of miniatures rules for the Napoleonic Wars from over 50 years ago, while you could see all the units on the table, their morale was not known until the first time you had to test it (and if there was a neutral Umpire present, not even then!). Since 'morale' was a set of three numbers multiplied together, one of which was based on the type of unit (Line, Guards, Grenadiers, etc) one based on you the General's estimate, and one a random generated by the Umpire or game when you tested, which might be 0, there was a chance that on its first test for stability your lovingly painted Franconian Militia might turn out to have 0 morale and run right off the table before you could stop them. It made for some exciting games, but also some frustrating ones. A vehicle for Perfect Plans it wasn't.
Which is the real Crux of the problem. Having the entire game buried in a computer means that virtually any information can be randomized, hidden, or manipulated to Mess With The Gamer's Mind, without needing an Umpire at all. This can give the gamer a taste of the Real Problems that Lieutenants, Colonels, Generals, Politicians, Diplomats, and even God Kings have to deal with all the time, but it may also make Ferd the Gamer rage quit after the umpteenth time he walks his scout into a field of digital bunny rabbits - who all happen to be Homicidally Rabid.
So, much as I like having to deal with 'real' historical Problems, including the fact that No one out of your sight can be trusted to do what you ordered them to do (Mary Beard's recent book on the Roman Emperors emphasized this: even the semi-Divine Imperator of Rome could never be sure that anyone was telling the truth or that anything out of his sight was actually being done the way he wanted it to be: picture of a gamer in a 'realistic' Historical Game!) - I think the whole concept has to be handled very, very carefully. While there is no real limit to the perfidy or apparent perfidy/randomness of people and Mother Nature (the Homicidal ***** of Goddesses), if All is Random the game is unplayable. And if most of it is unpredictable it is effectively unplayable except by Masochists.
So, leaning away from the Omnipotent, Omniscient God-King, Grand Nagus, Ineffable Rotundity is not a bad thing, and some 'uncertainty' can keep an apparently-certain game interesting, but the designers have to constantly be asking themselves: "Is This Too Much?" or "Can This Be Handled With Less F*****g With The Gamer?" Because too much of the latter leads quickly to No Sales and some really nasty comments about the game posted on every site from Tobruck to Togo . . .