I purchased a vinyl coated foam stadium seat cushion made of soft closed cell foam rubber dipped in vinyl and completely sealed and coated, to use on the DFW light rail. On longer trips, of 30 minutes or more, the seat cushion really helps, as those hard seats on the light rail trains are unforgiving.
But, when riding the TRE, the Trinity Railyway Express, then no cushion is need, as those sats are nicely padded.
I hope you enjoy your cushioned seat. New Jersey Transit buses have upholstered seats which are reasonably comfortable even though a bus bounces you around a lot more than light rail. However, there is a problem. The seats can harbor bed bugs which can get on you and into your bed at home. This has happened to people. So I prefer the absolutely hard plastic seats on New York subways and buses. I’ll trade the discomfort for the lack of risk of bed bugs.
But you have a good idea about carrying your own cushion.
I was initially going to say probably, but even though my weight is much more than it was before I retired, my wife says I have no butt, so I guess the answer is no.