You must not know many rich people if you think addiction is not an issue for the wealthy. The drugs of choice are less immediately destructive, but cocaine, pills, MDMA and ketamine are all wildly abused by the 1%.
All humans are susceptible to addictions and addictive behavior, but the 1% that you mention are mostly shielded from their negative effects. It's far less of an issue for them, and it's not even just about choosing the less destructive drugs. If we talk about just drug addictions, their wealth ensures that:
1. They always have a reliable supply of their preferred drug. No matter how much they need, many of them will be able to afford it pretty much indefinitely. They can just live with the addiction.
2. They have first-class healthcare to mitigate the addiction and lessen its side effects.
3. They have the power to never run into any legal trouble over it. How often do 1%s get convicted on drug possession? This often applies even to the harshest regimes.
So, referring to what the other commenter said, the wealth inequality also affects addicts unequally. The rich, excluding the most extreme exceptions, are immune to the downward spirals of addictions and many of their consequences. The poor addicts become increasingly desperate as their drug habit consumes most of their income and savings. The poorest turn to the cheapest, most dangerous street drugs. Many get little to no medical help. Many are charged with drug-related crimes, ensuring their criminality keeps them down for the rest of their lives. This varies by country, but the patterns are all similar.
There's always going to be an underlying layer of people who tend to gravitate towards addictions, rich and poor - the real question is if more and more people are turning to them as they get desperate, who wouldn't otherwise have.
