Totally not true. Simplest example: in F1 racing, they first allowed only 3.0 liter engines without turbo, or 1.5 liter ones with turbo. As the turbocharged engines wiped the floor with the naturally aspirated ones, they increased those to 3.5 liter, but that didn't make much of a difference. So they banned turbocharged engines altogether, as they expected that reducing their displacement and increasing that of the NA engines wouldn't make much of a difference in the long run, and be a losing game for the NA ones.The V8s in the G8 and charger all put out ~400 hp, with nice flat torque curves thanks the large displacement. There's no replacement for displacement, a 1.8l turbo 4 an never even come close imo.
Add a mechanical compressor as well, and you're for regular cars mostly limited by costs and emission standards and such, not by the maximum power attainable.
Edit: that 1.8 TSI puts out 180 hp on the stand, and can be chipped to about 230 hp without changing any of the other parts. The 1.4 TSI 118kw actually delivers 160 hp / 240 Nm (instead of 150/200 as I said before), does ~ 175 on the stand and can be chipped to about 220 hp.
The old 2.0 turbo engine of the Impreza could deliver close to 500 hp, if going all-out on the tuning and fitting bigger/stronger mechanical parts (like turbo, valves and camshaft) where needed.
Edit: or how about up to 800 bhp?
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