rnbqkbnr/pppppppp/8/8/8/3P1NP1/PPPNPPBP/R1B1QRK1 w kq - 0 1
I see that many players play Qe1, but why not just Re1? What is the difference? Doesn't the queen on e1 also make the potential weakness of a black battery from c8-h3 by exchanging the light squared bishops?
This might depend a bit on the black set-up.
One reason to play Qe1 instead of Rf1 could be that the rook will often be needed on the f file later to support the attack with f4...
Another example where Qe1 can make sense in the KIA is to support a knight on h4 when playing f4 as in positions like the following (which is fairly random) where white can recapture on f4 with the g pawn.
r1bq1rk1/pp1n1ppp/2nb4/2p1p3/3pPP1N/3P2P1/PPPN2BP/R1B1QRK1 w - - 1 1
One problem with Qe1 besides the one you mention is that the pawn on c2 is unprotected and could be attacked by black with Nb4. Playing a3 to prevent Nb4 is also not something white usually wants as it creates targets for black's queenside pawn storm attack.
One reason the set-up with Re1 is less popular could be that it loses a pawn in a certain quite common variation:
[FEN ""]
[Title "KIA with Re1"]
[Startply "15"]
1. Nf3 d5 2. g3 c6 3. Bg2 Nf6 4. O-O Bf5 5. d3 h6 6. Nbd2 e6 7. Re1 Be7 8. e4?
Do you see black's tactic?
After 8. ... dxe4 9. dxe4 Nxe4 10. Nxe4, white has opened the file allowing for Qxd1!, forcing the Rook to abandon the Knight and black ends the exchange sequence up a pawn.
The Objective of KIA from White is to attack on the K-side of Black where Queen is an essential piece and without it the attack cannot be carried out . When the Queen moves from d1 to e1 then after White plays e4 and then pawns are exchanged and d file gets open Black can do an exchange of Queens and neutralize completely with White . So it is important to secure the Queen and sometimes along with Rook on f1 and Queen on e1 White is able to prepare a pawn storm .
