Not enough thrust (i.e., too many engines)
Taking the lightest wide-body, the Airbus A310-200, its MTOW (max takeoff weight) of 144-164 tonnes is >2 times that of a Boeing 737NG at 65-85 tonnes. A 737 equivalent in MTOW in the prop world is the C-130 at 70 tonnes, and it needs 4 propellers.
So we are looking at 8 propellers for an A310-sized wide-body, or 4 contra-rotating propellers, already 6 too many either way for the airlines.
A comment claims that a turboprop engine can be designed as big as needed, what's missing is that the bigger the torque, the more blades are needed, which will essentially turn a prop into a fan. A relevant post is, 'How does a fan differ from a propeller?', where Peter Kämpf compares the disc loading of propellers and fans.
- Propellers on a C-130 Hercules: 259.25 kW/m²
- Turbofans on a small BAe 146: 4254.35 kW/m²
Propellers driven by piston engines are the most efficient, followed by turboprops, but they don't have the thrust of jet engines. Try and picture how many propellers would be needed to lift a Boeing 747. In the commuter/regional range of 100 passengers, turboprops have great efficiency, but go bigger, and fewer engines win.
On paper all is possible, the issue is making a civilian product that makes sense, in this case, number of engines. (Airlines care about the bottom line, the military not so.)
More parts is higher maintenance cost. For turboprops some figures are in this AOPA table from Oct 2016 (variable cost that incl. maintenance):
So capacity has little impact on the variable cost, unlike the number of engines.
Fuel economy (bomber vs. airliner)
Let's call the number of engines/propellers/parts, "A", and fuel economy, "B". For the airlines, "A" tips the balance when the number of engines exceed 2, i.e., that is why civilian turboprops are of the regional size.
Comparing 4x extreme-end turboprop engines with contra-rotating propellers (8 propellers in total like on the An-22 that's been suggested in a comment), with say 2x GE CF6 jet engines (like on the lightest wide-body airliner), when it comes to only "B", is a different question that requires context:
The reason why the Bear is turboprop powered (same engine as the aforementioned An-22), is because it's a long-range bomber with loitering in mind, not a short-range wide-body airliner as asked. Turboprops were also considered for the B-52.
Addressing other comments:
The A400M was suggested as a plane that makes it possible, it doesn't. Its MTOW minus OEW minus Fuel is 15 tonnes, or 115 pax + luggage and no cargo. Also note it's only 4 m wide internally, narrower than the narrowest wide-body, the 767 at 4.72 m. This is confirmed by its max troop capacity of 116, design-wise because most of its length is to accommodate a ramp.
Ignoring all that, it's still got 2 engines that the airlines can do without.
cargo compartment: width 4.00 m x height 3.85 m x length 17.71 m
A comment saying the C-130 is already wide, it is not. It's only 3.02 m wide on the inside. A 737 by comparison is 3.54 m. And wide-bodies start at 4.72 m, which allows a twin-aisle (2+3+2) configuration, one more seat than the 6 abreast single-aisle 737.
Build it lighter (composites): In the history of airliners, whenever progress was made toward lighter materials, wings are built bigger for more efficiency, and so is the cabin, because the airlines want more passengers for the same MTOW, otherwise they can't stay afloat. A prime example is the 787, it uses lighter materials, and ended up heavier than the plane it replaced, because its efficiency comes in part from the bigger wings.
Regarding the noise, military turboprops (and jets) are very noisy, but when it comes to passenger transports, turboprops match the jets. This research for example compared the noise level in the cockpits (one of the loudest parts of a plane) of similar-sized planes (A319 and Dash 8), and the turboprop was the quietest.