We value displacement a bit too much.
The Germans did not start WW2 with engines as puny as the Merlin. The DB601 was 2069 cu in, the DB 603 2715, the Jumo 211 was 2136, and the BMW 801 was 2562. Even the Hisso 12Y was 2196 cu in. Everybody knew that a single engined fighter needed at least 2000 cu in to be at least competitive, and that was the bare minimum.
What is not listed here is weight, which was much more important to the aircraft designers than displacement.
Engine.............................Displacement/cu................RPM.........................weight...........................power/altitude.
Allison.................................1710...................................3000...........................1325lb.........................1090hp/13,200ft
DB601A..............................2069....................................2400...........................1367lb.........................1000hp/14,760ft
Hispano 12Y-51..............2196....................................2500...........................1085lb.........................1000hp/10696ft
Jumo 211...........................2136...................................2300............................1356lb...........................975hp/15,585ft
Merlin III.............................1647...................................3000............................1375lb.......................1030hp/16,250ft
This in early 1940(?) things changed fast but the basic engines were there. Note that except for the Hispano the other 3 engines are within 50lbs of each other. They make similar power, within 100hp (10%) and similar altitudes (3000ft?) with the highest power engine (Allison having the lowest altitude).
Germans often used an extra 100-200rpm for take-off.
The Hispano is the odd man out. Lightest weight for greatest displacement and the lowest altitude by 2500ft. It needed major changes for either higher RPM or higher boost pressures (higher cylinder pressures). This is problem for the French in 1939-40 and 'what if' scenarios. The Basic engine was old and weak. While it was OK back in 1932 at 650hp the block and crankshaft/con rods were not up to the job of 1000hp +. Soviets added around 170-180lbs of weight and the Soviet engines were not noted for durability.
Germans increased RPM while Allison and RR increased boost pressure using better fuels.
Germans tried using their 96 octane fuel but could not make enough and had to resort to a lot more 'tricks' and finally the DB 605 of 2167cu in and 2600rpm (later versions could use 2800rpm for emergency power) but weight went to around 1670lbs.
Without the higher octane fuels Allison and RR had a bit of problem. Perhaps they could have increase RPM a bit. Perhaps (they did) increase the capability of the supercharger a bit even using 87 octane fuel. Perhaps they could had developed fuel injection.
But the two allied engines were robust, high rpm engines. The extra RPM allowed them to flow 25% more air per minute than a 2400rpm engine and that made up for a lot of the displacement difference. Allison went through 4 different crankshaft models from 1940 to 1944(?) with 3 of them being identical except for heat treatment, much greater fatigue life.
The last version got 27lbs more counterweight and was rated at 3200rpm. They had the space for it in the crankcase and you could put the new crankshaft in an older engine.
The DB 603 was 2,717cu in, it was also around 2030lbs.
The Vulture was 2592cu in but it was 2450lbs(?)
The Merlin XX and 45 getting around 10% more power 2,500-3,000ft higher than Merlin III tided the British over (and making 300-400hp more down lower) also helped cover over the failure of the 3 big British engines. The two stage Merlin 60 series and the full potential of 100/130 fuel propelled the Merlin to legendary status.
The 100/130 fuel allowed for cylinder pressures almost double what 87 octane allowed. And the Merlin was strong enough to take it without too much modification. The 2nd stage took over 200hp to drive and that power came out of the cylinders. Power being generated was lot more than the power to the crankshaft.