I currently store my collection in the same manner you describe above: Sleeves in boxes.
Binders and pages are going to be very, very bulky in comparison, and this is my primary reason for not pursuing this format. Never mind the cost of the binders and pages, nor the potential chemical concerns of the materials, which are secondary reasons.
With my current compact and efficient storage method, I can fit everything in my safety deposit box at the bank and keep minimal items at home. If I used binders, I'd need a whole shelving unit (well, lots of space in any case).
That said, each collector will have their own needs and concerns that need balancing and one collector's solution may not be appropriate for another. I hope what I've shared above has been insightful.
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BWJM, F.O.N.A.
Life Member of CPMS, RCNA, ONA, ANA, IBNS, WCS.
President, IBNS Ontario Chapter.
Treasurer, Waterloo Coin Society.
Show Chair, Cambridge Coin Show.
Fellow of the Ontario Numismatic Association.