Its then up to the writers to either revive that character or replace them with someone new.
If the writers were able to replace him with someone new, then why didn't they do so then? Or now?
Their decsion to keep Brock despite his apparent staleness means that they don't feel like doing what most of the fandom wants. Because they really don't need to.
They don't replace character for the sake of replacing characters. They only replace characters when they feel that the new character would be really popular with fans. Hence why they replace female characters. It's easier to draw a cute girl with a cute personality and stick her in the group then drawing a male character with no appeal and do the same thing.
Also, if a hypothetical character were to replace Brock, what is stopping him/her from doing the same things that Brock is doing now? If he's going to replace Brock, this hypothetical character would end up taking over nearly all his roles. We'll end up back at square one with a boring character. Why replace uselessess with more uselessness?
Also, the most interesting aspect that Brock can provide (aside from being Team Mom, which people assume that anyone can do), is that his Pokémon team can end up being very eclectic.
Ash usually ends up having a team that sorta fills the same roles as his original team:
1.Pikachu
2.The Flying Type (The main bird of a generation. Recently it appears that it's gaining a stalwart personality, and is quite loyal to Ash).
3.The Grass type (Now exclusively the grass starter. It's personality type appears to be stoic. They also end up being quite powerful battlers.)
4.The Fire type (Normally the fire starter, but it's trying to be more varied, even with the increasing fire types in later generations. They usually end up having something to prove to others.)
5.The Water type (Used to be the water starter, now filled in by others Pokémon. Their personality ends up being very fiesty.)
6.The Wild Card (Can be any type and any personality.)
the female coordinator now appears to be following a similar role filling. Somewhat:
1.The Bird Starter (Plays as the main batter on her team.)
2.The First Love (Ends up being her first capture, and a natural in contests.)
3.The Miscehvious one (Extremely cheeky, and is very cute.)
4.The Feminine one (Portrayed as a female, especially when compared to her unisex teammates and other members of it's own species.)
5.The Big Eater (Little explaination needed.)
and if the trend continues, she might get her own egg. This might become:
6.The Baby
Even Team Rocket follows a similar formula:
Jessie uses:
1.Wobbuffet
2.The Snake (A "Relic" member of when Team Rocket mostly had poison types.)
3.The Flying Insect (The main contest Pokémon as well, although all the Pokémon Team Rocket has may be used in contests.)
James has:
1.The APP (The Affectionate, but painful, plant.)
2.The BFF (The Best Friend Forever. Rarely battles, due to James being unable to see his friend getting hurt.)
and to top it off, they have Meowth, who's TR's counterpart to Pikachu.
Brock however, is free to catch whatever he wishes. Even though his team remains small. The best way to acheive his goal of being a top breeder is to take care of as many kinds of Pokémon as he can. This means having to raise Pokémon with very different needs.
Right now, he currently has:
1. Croagunk, which is not only a powerful fighter, but being an amphibian, needs to keep it's skin moist. It also comes off as confident and cool, but still competitive when pushed.
2. Sudowoodo, being a rock type, it needs to keep itself as dry as possible. It appears to be fun loving, and has grown up quite a bit from it's crybaby personality as a Bonsly.
3. Happiny, who's only a small baby, but has alot of strength. What sort of character development will it get as it grows? who knows.
All of this adds to more variety in Pokémon personalities. He's a good way to show off that characters don't need to follow old formulas to be useful. That's kind of his main draw. I however, would be satisfied if any replacement can do this job as well as Brock can.