It is a fairly significant investment both in cost and space to have compressor large enough to take the very low pressure distribution service (can be as low as 3~5 psi and compress up to 3,600 psi and at a volume to match constant fueling in short time periods.
If you start from a transmission line point of service, it is normally 1,000~1,200 psi. It is far lest costly to compress 3 times versus a 1,000 times increase in pressure. Far less horsepower required as well. A company running off a distribution line could hardly compete economically with someone running off the transmission line.
But transmission line service is far more limited locations. In many places in Texas, those lines are common. In New England, there is very few.
They also are going to need a decent amount of high pressure storage volume, ~4,000 psi capable to deliver to the 3,600 psi vehicle storage tanks quickly. So up those previous figures I just mentioned.
What you described can be done. But the amount of energy required becomes significant and the corresponding cost savings get smaller. People have to spend significant amounts to convert and likely loose significant range or storage space. They need to get significant cost savings in fuel or few will make the change.
So, perhaps locating the facilities along transmission pipelines, and running the compressors on uncompressed gas might work?
On the other hand, liquid fuels fabbed from NG might just be the next type of refinery to be considered. Here's a link I found on that topic:
natgas.info/html/gastoliquids.html