Yeah, this issue has been a thing in role playing games since the hobby began. The problem, I think, is that most roleplaying games, even the good ones, don't really allow you to be "Evil" per se, rather they let you be "Crazy".
The main issue, at least for me, is that I think most game developers don't really know how to write for truly evil characters. And to be fair, that's a very good problem to have, since if it were easy, that would be rather concerning. But because of that, the options they do give you are so over the top that it ceases to be evil, and instead just becomes insanity, which is different.
One of the few games I ever played which actually gave you some pretty good true evil options was Planescape: Torment. Wonderful game in it's own right, and while it certainly had it's share of Stupid Evil options, it also had many other, much more subtle options. But more than that, truly playing a realistic evil character requires you to be able to truly justify your evil actions, and justify them in a way that could actually have a decent case. Even the most evil people in the world didn't actually think of themselves as evil, people don't wake up in the morning and think "How many puppies should I kill today?" Unfortunately, realistic evil is actually not all that interesting for stories, but more to the point, if you wrote in options for a truly and intelligently evil character, that character would probably be OP.
In regards to your character being Chaotic Evil yet going out and saving puppies and kitties, well, you could always spin it so that your character is intelligently evil. After all, if you just went around and acted like how most people play Chaotic Evil (often poorly), your party would be ended pretty quick. So instead, you build up good publicity in order to buffer yourself and your reputation in the eyes of the public... all while proceeding to slake your evil lusts and desires on slaves you have shipped in from elsewhere. Or perhaps even something as simple as just taking an unhealthy amount of pleasure in the slaughter of your foes, even if those foes are, themselves, evil.
Overall, though, in regards to your issue, yes I think it's something that many role players struggle with. For the most part, being at least somewhat altruistic is a fundamental part of human nature, and a non-psychopathic person trying to act like a psychopath in games is likely to be clumsy at best. Which, of course, leads to players playing evil like morons, or failing at being evil altogether, because trying to do so in a believable way is instinctively uncomfortable, so we seek refuge in audacity.
Sorry, this was probably way more long winded than it needed to be
