Perry White has the same problem as most of the Daily Planet staff, he's a great well rounded character with a lot of potential who doesn't even get used for a hell of a whole lost besides filling the role of "Superman's boss when he's not being Superman." But I think he has it worse than some of the others. Lois is Superman's love interest, and while for pretty much the entirety of the Silver Age that meant she was stuck humiliating herself in uncomfortably sexist and ununny stories about her trying to win Superman's affections and him being an enormous ******* to her, as the years went on she really developed and basically graduated to the status of unnoficial co-main character of most of the Superman titles, especially after Clark revealed his secret identity to her and the two of them god married. After that she basically served the role as his primary confidant, and got a bunch of sub plots of her own involving her doing amateur detective/investigative journalist awesome stuff and even sometimes sharing the plot with Clark as she approached the problem from a non-superhero angle.
Jimmy, aswell, gets a little more spotlight because he holds the side-kick status by default. Yeah, Superman has had Superboy and Supergirl, but Jimmy's been around much more consistently, and in the case of Supergirl, well, maybe it's a holdover from the days of trying to copy Robin all the time but sidekicks of the same gender as the main hero tend to get the most spotlight. I still hold that Jimmy is underused and has a lot of untapped potential, but the fact is he's pretty consistantly there. When Clark hangs out with somebody outside of work, it's usually Jimmy. When either Clark or Lois are in a dangerous situation and they need somebody to talk to and do stuff for them, it's usually Jimmy. It's entirely a support role, and I think he's hindered in part by not being in on the secret, but at least he's almost always there.
Perry, though, he kind of drifts in an out. He had some really good storylines in the 90s, with his heart condition, his streined relationship with his son, His own rivalry with Lex Luthor that paralelled Superman's rivalry with Lex, his adopted son dying, his serving as Lois' surrogate father. All good stuff, but it kind of came and went, and was mostly limited to the early-to-mid 90s. And with a franchise that has as long a history as Superman, that's kind of a flash in the pan.
I think the big problem is the continuity-less nature of Superman. I mean, yeah, there's a continuity, but only because writers usually don't disregard what came before (excepting the damned recent reboot). Superman, like most of DC comics, lacks any kind of narrative focus or goals. Superman flies around and does stuff. Sometimes it's interesting stuff, sometime's it's boring stuff. But none of that stuff can really change anything of value so the next writer can still play with all the toys. It took over half a century to get Lois and Clark married, and they had to drag that out kicking and screaming. It's probably why Lois is Superman's best supporting character. She was allowed to grow, her relationship with Clark actually developed, her story went somewhere and had a purpose. Until Grant Morrison decided to be a nostalgia *****e and bring back the love triangle because all of those vaguely sexist sitcom hijinks had so much literary value and had so much more material for telling stories than a well developed commited romance.
But that's another rant for another day.
The point is that Perry is purposeless. He's just there, being Superman's boss who yells at him sometimes. He has a backstory, he has a lot of personality, he has a lot of things that could be done with him, but nothing is being done with him. If Superman were a story with tight continuity and an actual narrative goal, I think Perry would be a fantastic character.
It's why I think Superman, and most mainstream comics franchises, need their own Once and Future King treatment. The story of these characters, taking the best parts of all the different versions, finding what untapped potential of the core premise there is left, finding what the character and their story is about at the core and making that the focus, and telling a story with a clear beginning, middle, and end. It doesn't have to replace normal comics, it shouldn't, but it would be a wonderful suppliment. It's what the new 52 could have been, but we all know that it's not going to be like that at all.
Alas.