There are a lot of trial sets with varying effects.
I would not say that no trial sets have use in solo builds or PVP.
PVP builds vary a lot, and there are certainly some builds where some trial gear is very useful. For example, recently there were a lot of complaints about Relequen (drop from cloud rest trial) being too strong in PVP.
A set like Master Architect (drop from halls of fabrication trial) is very useful in 4 man dungeon groups.
Interesting that you describe solo trials (arenas?) and PVP as "general purpose", but trials are not "general purpose". If you are a player who likes to do trials all the time, then trial gear could be considered general purpose.
However, if you don't want to do trials, only solo and PVP, then you can certainly do well without doing any trials.