One of the best reasons for my predilection for such a formula is surely in my previous posts about engines:while the Americans, constrained by the fuselage dimensions had to modify heavily the engines of their own legacy planes in order to increase their thrust, ending up with just a modest increase of the final T/W ratio but completely screwing their own bypass ratio, the pod configuration allowed instead russian to increase the fan diameter of the Al-41-117S in order not just to retain but even to increase the Bypass ratio together with the T/W one compared to the original engine.
Same will happen with the Al-51 on Su-57: they would have a way better engine that would actually be even more compact than the actual one
Apart from leaving a very usable space for the bays, it surely has advantages in survivability and accessibility to the engines, in that regard I like a lot this picture of the Su-57:
You can see the completely unimpeded access to the engines and ancillaries, as well as the way engine is minimally surrounded by other systems that could be damaged in case of an engine failure.
As to the increase of BPR, are you sure the izd. 117 has a bigger total diameter than AL-31F? I know the compressor is a bit bigger, but I thought the engine overall kept the same external dimensions.