Is it because cold thrust reversers are best for turbofans and most civil airliners have turbofan engines?
Smaller airplanes with both rear-mounted and under the wing engines used to have "bucket" type reversers, which captured both hot and hold exhaust. However, a bucket is not a tenable solution for large diameter engines. Fortunately, in modern turbofans the cold thrust is the vast majority of the trust, so there's no point in trying to create a bucket large enough. Therefore, axial designs became prevalent.
First off, all civil airliners nowadays use turbofans, not just "most".
Second, almost all civil airliners still in service use specifically high-bypass turbofans, with a bypass ratio1 of 5:1 or greater. With these engines, the vast majority of the engine's thrust comes from the cold bypass air, not the hot core air, so, even if you reverse both the hot and cold streams, you'll only get a little more reverse-thrust decelerative force than you would if you reverse just the cold stream (leaving the hot core exhaust untouched).
Jetliners using low-bypass turbofans (bypass ratio under 5:1, and usually below 2-3:1) generate a larger portion of their thrust from the core exhaust (in most low-bypass engines, the core exhaust produces the majority of the engine's total thrust), so, in order for reverse thrust to generate a useful decelerative force with these aircraft, you have to reverse both the hot and the cold exhaust streams.2 However, few of these aircraft remain in service, due to the high fuel consumption and noise production of low-bypass turbofans.3
Most first-generation high-bypass-turbofan-using jetliners did have reversers for both the hot and cold exhaust streams (known as turbine reversers and fan reversers, respectively), using a number of different systems for doing so. However, reversing just the cold bypass stream proved to have some important advantages:
- On high-bypass turbofans, most systems for reversing both the turbine and fan exhausts use separate reversers for the two. This doubles the number of mechanisms which maintenance has to keep in working order, and doubles the opportunities for things to malfunction reverser-wise. (On the plus side, this also made it easy to remove or disable the turbine reversers while keeping the fan reversers fully operational.)
- Turbine reversers have to handle the exhaust gasses from the engine core, which are:
- really really hot,5 and
- loaded with delightfully-corrosive combustion products and surface-eroding soot particles,
- both of which cause turbine reversers to wear out much more quickly than the fan reversers,
- decreasing reliability and requiring more frequent maintenance compared to the fan reversers.
Since the turbine reversers provided only a little additional decelerative force (remember, the vast majority of a high-bypass engine's thrust comes from the bypass air), deactivating them resulted in only marginal increases in stopping distances, while greatly alleviating the maintenance headaches associated with the reversers.8 Later generations of jetliners with high-bypass turbofans omitted turbine reversers entirely.
1: The ratio of the amount of air that goes through the bypass duct to the amount that goes through the engine's core.
3: The only low-bypass jetliners still in relatively-common use (and mostly in third-world countries at that) are the DC-9-80 and 737-200, and even these are being retired by the day. Low-bypass turbofans remain somewhat more common on business jets, but are slowly being superseded by the newer crop of high-bypass bizjets. The only area in which low-bypass turbofans aren't losing ground is in military combat aircraft, where their loudness and thirst are less important than their rapid throttle response4 and their good performance in supersonic flight.
4: High-bypass turbofans have heavy, large-diameter fan rotors, which take their sweet time to get up to speed. The smaller fans of a low-bypass engine have much less angular inertia, allowing the engine to accelerate and decelerate more quickly.
5: Even the "cold" bypass air of a high-bypass turbofan is still quite hot by human standards, due to the considerable amount of essentially-adiabatic6 compression produced by the whirling fan (which is also known as a low-pressure7 compressor; not only does it fling air down the bypass duct, it also helps precompress the air going into the core); however, the core exhaust, having been subjected to compression not only from the fan but also from all the other compressor stages, and then used to burn fuel in the combustion chamber(s), is much hotter still.
6: Adiabatic compression is compression that occurs quickly enough that there's no time for heat to leak into or out of the stuff being compressed, which is a pretty-good approximation for what happens to the bypass air in a turbofan.
7: "Low-pressure", here, is very relative.
8: In this respect, the story of turbine reversers is reminiscent of that of nosewheel braking - another deceleration system fitted to some early jetliners, found to be more trouble to maintain than the marginal improvement in stopping distances it provided could justify, and, consequently, disabled or removed.