Yes and no. Turbocharged engines tend to be less reliable than naturally aspirated ones but it's actually rarely the turbo that's the failure point. After all, diesel engines are more reliable than gasoline engines and all diesel engines have turbochargers.

The reason for this is that diesel engines are made to be much more robust than gasoline engines due to the much higher compression and energy of diesel fuel. They can easily take the stress of a turbocharger with no issue. Gasoline engines on the other hand are not quite as sturdy.

The main issues stem from the increased stress on the engine and the higher temps. Increased cylinder pressure stresses the piston rings and rods more, as well as the headgasket. Higher temps are also bad for the headgasket and also for the oil and cooling system. Also, while the turbo itself is rarely the failure point, it's part of a whole system that just introduces a bunch of extra failure points. If the wastegate actuator fails, it takes the turbo with it, same for boost control solenoids. Boost pipes may leak. The intercooler may crack. All those things are not present in a NA engine.

The turbo itself is actually quite robust and only has one failure point, its shaft. The bearings and oil seals on that shaft are the main things you have to worry about. The best way to keep a turbo happy is to stay on top of oil changes, keep your air filter clean, and ideally, if you want to be extra safe, idle for 30-60 seconds after parking before shutting off the engine, so that oil still circulates and cools down a bit before you shut the oil flow off. Scalding hot oil on the turbo can cook the seals and bearings. A few more minutes if you were driving hard.

Of course saying it like that makes it sound like turbos are a really bad idea. They're not, and obviously engines designed for turbos are degined to take those loads, but they're closed to design limits compared to diesels. The main reason is because usually when a manufacturer decides to put a turbo on an engine, they also downsize it. So when they might have once used a 2-3L for 200 NA horsies, now they have a 1600cc turbo engine for the same power output instead.

And if you're wondering why manufacturers don't just make gasoline engines more robust like diesels the answer is cost. They used to, now they don't. It's the reason why engines like the 2JZ are so popular. That's an engine that's reinforced from the factory and the stock power output does not even come close to stressing it, which is why it's so popular for performance upgrades. At the time Toyota wanted to put out a sportscar without jeopardizing their reputation of reliability and the solution was to overengineer the engine to make sure it could take it. Nowadays with modern modelling software available and an emphasis on cutting down production costs manufacturers are cutting it closer to design limits.