I started off playing in Beta in solo mode, while I got to grips with the game, but then quickly reverted to open play. Most of that time, I'm happy to say, has been more enjoyable.
I decided to only trade in a defensible ship (in my case, a Cobra initially, and now an Asp) due to the constant threat of being pirated on my rare trade route (especially around Lave, Leesti, Orrere, etc - surprise, surprise). I wanted to be able to defend myself, should the worst happen. Occasionally, NPC pirates would interdict me, but escaping them wasn't especially hard. However, my encounters with other CMDRs have been mostly thrilling.
The first pirate player to interdict me asked me to help him provide for his 6 kids! Hmm, I was not feeling overly sympathetic or generous, so quickly boosted away. Due to being mass locked, that wasn't so easy... So, several laser blasts and shield cells later, I was unfortunately only left with 53% of my hull; but I escaped and was also left with the feeling of a moral victory ("What's mine is mine, pirate!"), the sound of my heart pumping in my ears and the feeling that I had experienced something truly different and special.
I do understand the argument that trading in open play is a risk and, quite possibly, an unnecessary one, since everyone has the choice to play open or solo. However, I would suggest that playing in open play is potentially the most rewarding way to do it (and I'm not talking credits). Sure, it could depend partly on what ship a player is flying, how defensible it is and how much he stands to lose, should the worst happen. If he is flying a fairly weedy hauler or poorly defended transport ship with an expensive cargo, that risk would seem to be too much. It would certainly shred my nerves if I had sunk a lot of time, effort and in-game credits into a trading run that was in danger of being wasted by a random act of violence, or even an accident. Yet, this is still part of the experience.
Trading under these circumstances gains something in open play - that feeling of uncertainty while travelling, of adrenalin while barely escaping a would-be pirate and the relief of reaching your destination and the safety of a station. Of course, there may be frustration too, but such is life - we can't have it all our own way, I guess.
Plus, if a particular location seems to be a haven for players trying to spoil the fun, it could be advisable to move to a different part of the Galaxy. After all, it's a big playing field.
TL : DR - don't give up on open play. Solo play has its merits and I am glad it exists, but open play (and, indeed, private groups) adds something to the experience of Elite Dangerous that can be truly memorable.