Yes PNG is not Lossy, it is a newer format than most of the other formats.
It was design to be a replacement for GIF due to copyright infringement
issues with the use of GIF.  And yes it has the capacity to go to 24-bit
(8bit/chan) and even 48-bit(16bit/chan) color rendering.   But where do you
need this?  Websites will bog down with servers trying to render images at
8bits per channel. GIF is used primarily for images that have few colors
that can be rendered in less than 256 colors. And as I discuss later it is
not as widely accepted for printing.

Yes PNG offers transparency and when that is needed with more color
requirements than GIF can handle by all means use it.  However transparency
is not supported in older versions of web browsers and is therefore still
limited in its use.

As far as printing is concerned while most consumer places for printing
will take jpeg and process them professional printers us TIFF.  TIFF
supports more print formats and more printers support TIFF than all other
formats combined.  As a professional printer you risk losing money
accepting jpeg as a format.  If you can't guarantee that your prints will
translate from file to print you will lose money on reprints.  I once
watched a pro photographer and a printer argue for 30 minutes over a single
print.  In the end the printer was forced to reprint a 26" size print over
at his own cost.  If you consider his time and the lost materials in ink
and paper that 30 minutes cost him $150.  As an engineer I have sent design
plans, 200 sheets at 24x36 inch size and requested 25 sets be printed, and
asked for them back in 2 hours. The only format the printer will accept and
guarantee delivery in that time frame is TIFF.

As far as the COSCO print example these are all first generation copies of
the jpeg.  If you were to open and save these files sequentially it will
degrade every time it is reopened and re-saved. That is why professionals
do not use it.  They need to be able to have on hand upwards of 10 to 20
different versions of the image for different uses in digital and print
media.  By the time the final images go to print and the sites go live that
file has been opened and closed over 100 hundred times.  If jpeg is used it
is only used as the final image.  If there are any edits the image is
manipulated in a different format.

For most people's needs jpeg is perfectly adequate. However if you want the
most control over your image both in the camera and during post processing
you will only shoot in RAW.  Cameras that shoot in jpeg or even TIFF
formats are still making choices for you.  What is the point of buying a
DSLR, setting it to manual, fine-tuning, fstop, shutter speed, ISO, flash,
and the compensator only to have a computer algorithm make the final
decision as to what to save and be limited in can change it later?  With
RAW every pixel is recorded exactly as the sensor saw it.  More often than
not I can fix noise and blown out areas with the information from RAW.  In
jpeg or even TIFF you are out of luck.

I equate cameras with RAW like sitting at the Linux command line making
every decision with fine-grained access. While JPEG is like sitting at
other operating systems with less access and final control.  Just my two
cents.

-- 
James