Well yes there are certain starts and events that make it more likely. You can do things like keep a royal marriage without an alliance so you are ready to claim throne & war straight away.
What I find is that as the game goes on your high value PU options become increasingly limited. Some rival you and some aren't willing to royal marriage you because of low relations for a range of reasons. Diplo relations are also a thing. I'm sure you could get some HRE princes semi-consistently if you kept an eye out.
E.g I'm coming up to 1700 on a Prussia/Germany run. Luckily I got the von Wittelsbach dynasty which I purposely chose when I had an old general king with no heir. I'm pretty sure Austria was going to PU me if I royal marriaged him. A 6 province Bavaria had a 70+ king so I PU'd him, and later on I forced one on Norway coz I made it happen. Nothing special though. Now that I think of it I probably should have gone for a different dynasty but I was at risk of being PU'd myself and now I remember I was trying to PU Denmark. Unfortunately he eventually turned hostile.