Go for it!!
Even though I am far from retirement and am a single male -- I do travel solo on most of my Amtrak trips... and never had any serious issues. The main reason for solo travel is that most of my friends are all about "getting there quick" and dont appreciate the fun or excitment of Amtrak travel. Really, I can only think of one friend of mine (who I met through AUF 4 years ago) who would actually want to accompany me on a cross country loop-de-loop for a week straight on Amtrak. Most of my 4 weeks of vacation every year are just taking a train trip somewhere. I have been to most of the major US cities -- so I am enjoying the journey there and the time of the train more than the time actually off the train.
Anyway, I think you will have a good time.
You will almost always be safe on the train itself -- just watch yourself at some stations safety-wise. I never had any problems except for people begging for food or money in Chicago, LAX, New Orleans, and NYP.
One other tip -- if you dont want to be social all the time -- think about getting a sleeper. While most of the time I like talking to people and spend most of my time in the lounge car -- it's nice to have your privacy if you get sick of talking to people -- that way you have your own little "home" to go back to when you want to be alone. If you are in a packed coach, you might have that option just to get away from everyone else.