Since jet fuel is cheaper, why do pistons still use av-gas? Why is 100LL used at all?
First off, there are some light aircraft powered by diesel like the Piper Archer DX and the Diamond DA42. It should be noted both come in a 100LL powered version as well. As it stands now the FAA is looking for a replacement for 100LL but has not yet decided/found one. There are also some airplanes out there that can run on mogas. But anyway, more to the point, you cant simply put diesel into a regular engine as the ignition system and compression requirements are different. Thus to convert a plane to diesel you need a different engine all together. With that in mind most certifying bodies dont just let you swap airplane engines to any engine you see fit. The engine would need to be certified for the air frame which is a costly proposition. Thus it is sensible and economical to keep the current engines running. There are some efforts like those made by piper and diamond to slowly make diesel aircraft available.
As to why 100LL is used, this stems mostly from history. The vast majority of the general aviation fleet both physically and simply in design, stems from the dawn of the jet age. When the lines for the 172 were first drawn there was plenty of 100LL to go around, it was for lack of a better term, the logical choice.
TL:DR: Jet-A is cheaper than 100LL, but the support systems and availability are not yet in place to make engines that burn Jet-A an economical choice for private owners looking to retrofit their existing airplanes in the US.
While the fuel type may be cheaper, the cost of retrofitting an airplane with a diesel burning engine is not. With the price delta between AvGas and Jet-A, it takes a (reasonably) long time (if you're not a flight school or active club) to recoup the cost of the engine retrofit.
There are some additional considerations, such as the chicken-and-egg scenario that small airports often only stock 100LL, limiting where you can fly (if you hope to fill up on arrival).
It's frustratingly difficult to find current new prices (everyone wants you to "call for price"), but the ones I could find show a $116,000 difference between the Jet-A burning Skylane and the 100LL one (2013 and 2012 prices, respectively).
Skylane JT-A base price \$515,000 Skylane T182 base price \$398,100
So it would still take a while, even with a new plane to recoup the additional cost.
André Teissier-duCros, a former SMA consultant...published an analysis in August  comparing various flight school business scenarios. Teissier-duCros calculated (assuming a price break of 59 cents per gallon on Jet A compared to avgas, and a two-year replacement cycle, among other things) that a used gasoline-powered Cessna 172 or 152 would break even at 150 hours, while a Cessna 172 Jet-A conversion (from either Premier Aircraft Sales of Florida or Redbird/RedHawk in Texas) would require 325 hours to break even. Beyond 600 hours, aircraft burning Jet A begin to generate more net profit for the operator than avgas alternatives...
Outside the US, however, AvGas is extremely expensive and can be hard to come by, so their is definitely a greater demand for these types of engines in airplanes outside of the US.
A Flying Magazine article from 2013 offers this explanation as to why our diesel future is still a ways away:
Still, no matter how good the technology becomes, diesels won’t supplant gasoline engines in America anytime soon. One reason is the sheer number of gasoline piston engines out there, flying in everything from aging Cessna 150s to brand new Cirrus SR22s — around 225,000 of them in all. Another is the continuing dominance of gasoline engines in nearly every production piston single and twin sold today. And many smaller general aviation airports throughout the United States sell only 100LL avgas, limiting where you can fly a jet-A-burning airplane. Also, because they lack an ignition source to keep their fires lit, diesels are restricted in how high they can fly, even with twin turbochargers and hot glow plugs — although this too could be a temporary issue that goes away as diesel experience is gained.
An article from AOPA in 2014 indicated some of the prices to replace the AvGas burning engine in an airplane:
A CD-135 costs \$55,000 to \$60,000 in a gasoline engine replacement scenario (a Cessna 172 replacement engine), including all necessary parts (such as a new propeller, engine instruments, engine mounts, and other parts) depending on the aircraft, while the CD-155 costs \$63,000 to \$70,800 for the same initial installation kit (dollar amounts converted from Euros). A replacement CD-135 costs a little over \$40,000 (excluding taxes, shipping, and labor), while the replacement CD-155 would cost just under \$46,000 (with the same exclusions).
Cost of replacement engine (Diesel): $51,150 Inspected gearboxes (3): $23,500 ($47,118 new) Shipping: $1800 High pressure pump: $1412 ($5550 new) Rail valve: $651 Feed pumps (3) $1255 Clutch (3) $1443 Clutch shaft (3) $1200 Alternator: $1426 ($2985 new) Scheduled labor $1800 Unscheduled labor $5000 Total: $90,637 Hourly engine (1200 basis): $75.53 Total hourly with fuel: $101.03 Lycoming IO-360 REM Cost of replacement engine: $25,160 Top overhaul at mid-time: $8000 Unscheduled maintenance: $5000 Total: $38,160 Hourly engine (2000 hours basis) $19.08 Total hourly with fuel: $59.58
One could compare this to a similar analysis that you might do when considering a hybrid car vs. regular gas-only engine. When is the pay-off for using less gasoline compared to the additional base price of the car?
Because nobody wants to buy expensive new engines for their 40+ year old planes? Because there's a significant cost to developing & certifiying diesel engines for light planes, but only a limited market? Because the cost of fuel is only a small part of the cost of buying and operating a light plane?
OK, since you want some numbers, Google gives the cost of a new Lycoming O-360 as around $80K, e.g. http://www.airpowerinc.com/productcart/pc/TLEngineDetail.asp?catID=33&prodID=453144 I haven't found prices for a diesel equivalent, but
one might reasonably expect the cost of an equivalent certificated aircraft diesel to be at least similar. Indeed, this article https://www.avweb.com/avwebflash/news/Lycoming-Diesel-Details-221664-1.html says "...a certified civil diesel engine would cost more than twice as much as an equivalent gasoline engine...".
Now if you check Trade-a-Plane for Cherokee 180s (I use this as an example because it's my plane), you find them going for $30-55K: https://www.trade-a-plane.com/search?make=PIPER&model_group=PIPER+CHEROKEE+PA28+SERIES&model=CHEROKEE+180&s-type=aircraft
Now why would anyone spend the (Dollar sign)80K it would cost to put a new diesel engine in a (Dollar sign)40K plane, in order to save a few bucks an hour on fuel? Or if we're talking about new production, why would manufacturers increase their manufacturing cost by maybe the same $80K?
PPS: If it's the cost of 100LL that's a concern, many light aircraft can run on mogas. There's an STC for the Cherokee 180, which we applied many years ago.