I have been following Arnies career a bit, being interested in weightlifting for several years and such, for many years. Most of his films, if not all, are quite watchable, even the first ones (Hercules ..).
He is by no means a great Actor, especially when speaking (no real emotion in his voice; more emotions conveyed by his "look" and mannerisms) but he never seems to take himself too seriously in his films, which is good and makes for a likeable character and entertainment.
As for being self-obsessed, considering his bodybuilding background, being considered a “looker” for decades and what he has achieved it is understandable. Apart from his “indiscretions

” he seems alright for what he is; a big celebrity/politician.