Q: Doesn't running boost on an engine put more strain on the engine's parts?

A: Not necessarily. RPM is what kills engine parts. Typically, an unblown engine has to run up to 7,000 or 8,000 rpm to make any real power. At these high speeds you need a special crank, rods, pistons, rocker arms, valves, valve springs, and on and on. But a blower substantially increases power and torque at much lower rpm's. You usually don't have to run a blown engine over about 6,000 rpm to make maximum power. At these speeds stock engine components are usually more than adequate.
Additionally an engine sees maximum load on the components at the moment the piston changes speed from going up in the cylinder to going down. There is a commonly held theory, too complicated to go into here, that increasing the combustion pressure, which a supercharger does, actually reduces this maximum load when piston travel changes from up to down. Under this theory, at comparable rpm's a blown engine is easier on parts than an unblown engine.
In actuality, as long as detonation is controlled, you rarely have any engine failures with a blower