So, what is Bug-type's role, really?
The Legendaries and Their Role:
Genesect is a cybernetic insect that serves as Team Plasma's Mewtwo. Its cybernetic design seems to inspired by the cybernetic enemies of Mother 3. It can turn itself into a disc, and was contemporary with Kabutops, which it shares design characteristics with.
However, Genesect's period of life more accurately refers to carboniferous period(358.9–298.9 million years ago), a period of the earth were arthropods reigned supreme as megafauna. Insects themselves have evolved 400 million years ago from crustaceans.
Buzzwole & Pheromosa:
Buzzwole & Pheromosa seem to be references to The Fly and Metamorphosis respectively, and their designs are supposed to be inverse of their animal designs(strong fly, clean cockroach).
The Trainers and Their Roles:
"The Walking Bug Pokémon Encyclopedia", he is a Bug-type expert who in original GSC found Fury Cutter move. He is based on a bug catcher kid with camper aesthetic, and he represents boys declining interest in weird animals as they grow up.
Aaron is basically anti-Bugsy. He looks like some weird Japanese pop artist and constantly talks about beauty of Bug-types. Much like Bugsy, he started as a Bug Catcher who became a Gym Leader, but got bored and became an Elite Four member.
"Premier Insect Artist" he is fascinated by the efficient anatomy of Bug-types. He was originally from Nacrene City and a pal of Lenora before he made it big in Castelia.
"The camerawoman who never lets a single smile escape her focus." she is the earliest of Bug-type trainers. She represents the theme of "different perspectives" of XY.
It's ya boy.
Guzma's association with Bug-type is more symbolic than anything else, especially since he doesn't use Bug-types in Battle Tree exclusively or even primarily(he has more Dark-types than Bug-types in Battle Tree). Apparently, Guzma was a promising, but rather weak trainer who couldn't reach to his goal of becoming a Trial Captain, implied to be under Hala's leadership. Because of this, and due to his abusive father, he escaped his home to find a similarly abandoned kahuna, whose identity is unknown. When that ex-kahuna was punished by guardian deities, he had to reform Skull in his own image. Because Lusamine was the only adult who recognized his talents, he became loyal to her.
His association with Bug-types represents his desire to be intimidating and strong, while being unable to do so. His association with his signature Pokémon, Golisopod, refers to how he always runs away from trainer after being defeated, but tries to keep face by simply walking away, as a tactical "emergency exit".
The few Bug-type legendaries are not really deities, just overpowered members of the type, enhanced due to sci-fi nonsense.
For Bug-type trainers, we have some variance. There are artists, generic trainers, regular Bug Catchers etc. However the overall encompassing thing about Bug-type trainers seem to be the same as Ice and Normal-type trainers, they have a desire to train further. But unlike other types, Bug-type trainers seem to be locked in whatever they are doing now and cannot really go further even if they want to. Bugsy cannot comprehend other types, and doesn't want to because it would mean he would grow out of them. Aaron cannot become the Champion or a higher leveled Elite Four because he sucks. Burgh doesn't really get the anatomy of other types. Viola is stuck with her role as the first Gym Leader and cannot really defeat her opponents because it would mean she wouldn't capture their smiles. Guzma tries his hardest but cannot grow with his type, so he changes up in Battle Tree.
All of these showcase Bug-type's inherent lack of power to accomplish its goals. Nonetheless, its abundance means it can see variety of forms.