Japanese aircraft armament was a complete mess that makes no logical sense is the short answer. Did you know that the 20mm Type 99-1 and 20mm Type 99-2 aren't developmental marks of the same weapon, but two completely separate weapons that fire completely different ammunition? I've seen the two side by side in a museum; it's quite shocking how different they are in terms of size.
There was no single Japanese 7.7mm cartridge. There were three; the rimmed, semi-rimmed and rimless. The IJA hated the IJN, and both hated standardization more than each other. The 7.7 rimmed cartridge is a clone of the British .303 cartridge (possibly interchangeable?), while the 7.7 semi-rimmed was used in the IJA's Type 89 fixed and Type 89 flexible (which are not the same gun in different mounts; one is a license-built Vickers design and the other is an elaboration on the Type 11 light machine gun with a belt-feed magazine clip mechanism [no seriously]) and the TE-4/Type 89 Flexible single gun (which is not the same gun as the other Type 89 flexible). The 7.7 rimless is the Japanese 7.7 round that most Americans are familiar with owing to the large number of Type 99 Arisaka bolt-action rifles chambered for it on the market.
That's not to say that the Japanese never adopted foreign guns to fire their own ammo. The IJA adapted the Vickers E class machine gun to fire the 7.7 semi-rimmed round, but the Vickers machine gun uses a link/belt design that first withdraws the cartridge rearwards before ramming it forwards into the chamber (much like a Browning or PKM), which means that it is a very suitable design for firing rimmed or semi-rimmed ammunition. The MG-15 and MG-17, on the other hand, use a double-drum magazine and a push-through link design, respectively, and both of these designs are tricky to get to work with rimmed or semi-rimmed ammunition. The IJN kept their E class clone (the Navy Type 97) in 7.7 rimmed because standardization is for wimps and losers.
So the 7.7 rimmed and 7.7 semi-rimmed were probably both too much trouble to be worth adapting either the MG-15 or MG-17 feed systems to. What about the 7.7 rimless round? Well, it probably would have worked, since the 7.7 Arisaka round is broadly a similar size and power to the 7.92 Mauser round, but the rimless round was still under development when the various and sundry clones of the Germans rifle-caliber machine guns were adopted!
