They could throw in a cat, dog, or deer (or even a sheep) instead of the rodent
Funny thing is, Gen 5 actually did this. Lillipup and Purrloin are both early route Pokémon in BW1 and BW2: the former is a dog, and the latter is a cat. Stoutland takes after Pidgeot and Staraptor in that it's a three-stage evo line that acts as a quasi-starter of sorts, evolving once at Level 16 and again in the 30s. Liepard is like the rodents in that it evolves once at Level 20 and has a BST closer to them (420) and is designed to be one of the weaker Gen 5 mons who falls off eventually as the game goes on.
Problem is, despite having Liepard and Stoutland, they
still felt an obligation to have a rodent and a bird exist alongside them too. They still put in Patrat and Pidove despite the dog and cat already fulfilling the early route introductory mon slots with a new spin on them, and they put them in there and made no attempts to make them interesting or unique: Patrat and Pidove are a huge step down from Bidoof and Starly who were actually fun and interesting both in-game and design wise, and to this day Patrat and Pidove are still the most boring, useless, and uninspired of all the generational rodents and birds. It's no surprise that they are, to this day, considered the worst of their respective archetypes, even worse than Rattata and Pidgey in some respects. You could get rid of both Patrat and Pidove from the Gen 5 roster and just keep Lillipup and Purrloin and you really lose nothing of value in the process.
Gen 3 even put in a Dark-type introductory Pokémon before Liepard ever existed in the form of Poochyena and Mightyena who are hyenas. Even so, Linoone still exists alongside it. Granted, Linoone is kind of an interesting Pokémon both design wise and in battle, unlike Watchog, so I can let Linoone slide.
Also, if they just so happen to make a 3-stage bird or bug, or a 2-stage rodent, what would they have to do with them to not be counted as "gen bug/bird/rodent"? Be good? But we've gotten gen bug/bird/rodent that are "good" yet they're still considered the gen bug/bird/rodent.
Generally the archetypes you mentioned are available on the very first few routes of the game. No matter how good or bad they are, they are among the first few Pokémon you will ever meet on your adventure, and have commonalities that define their archetype. Even with the variations within the archetypes, they all have similarities.
The 2-stage rodents/mammals evolve once at Level 15-20ish, have around 420ish BST (except Greedent), and are generally at their full potential early but fall off, being one of the weaker fully evolved Pokémon in the long term. Diggersby may be "good", but it's still a generational early route mammal in that it follows the other trends and has a low BST (it's only good because of its Hidden Ability, in-game it still sucks and falls off).
The regional bird archetype is also defined by being in the first few routes of the game. It's a Flying-type that is obtained early.
That being said, there are really two sub-classes of the early route bird archetype over the generations:
The Pidgeys: Pidgey, Starly, Pidove, Fletchling, Pikipek, Rookidee
The Spearows: Spearow, Hoothoot, Taillow, Wingull
It's important to remember that Gen 1 really had two types of early route bird: Pidgey and Spearow, but both are very different. The former class are the Pidgey sub-archetype: 3-stage early bird that evolves once at around Level 14-18 (21 in Pidove's case), then evolves again in the 30s. These Pokémon also tend to be in the Medium Slow exp group (Pikipek being an exception). These Pokémon are designed as a quasi-starter of sorts, evolving around the same time as your starter and serving as a Pokémon who is viable enough to serve your needs through the whole game. While you will inevitably ditch your early rodent/mammal and bug, the Pidgey sub-class of bird is a Pokémon you will probably keep and use throughout the whole game. This makes them highly desirable candidates for a team, as
these survey results have more or less shown, since Pidgeot, Staraptor, Talonflame, and Corviknight all achieved high amounts of popularity in their respective games as the most used team pick.
On the other hand, the Spearow sub-archetype is a 2-stage bird that evolves once at ~Level 20, and tends to have lower overall base stats than those in the Pidgey sub-archetype. They are almost always in the Medium Fast exp group (except Taillow) and are a bit weak compared to the Pidgeys, and they will probably fall off later on and be replaced by something better like Dodrio or Altaria, making them closer to the rodents.
Gens 2 and 3 had Noctowl, Swellow, and Pelipper who lean entirely on the Spearow sub-class, while every Gen since 4 has had a bird that takes more after Pidgey, being a three-stage evo line that acts as a quasi-starter and grows with you over the adventure.
As for the bugs, it is also them being on the first route, that being said, they have deviated more from the early bloomer gimmick that the older first route bugs have had. Vikavolt and Orbeetle are both on the first route of their respective debut games but reach their full potential later while they are strong enough to be viable late in the game. Leavanny and Scolipede *sort* of fit the archetype for Gen 5 but they evolve quite late: that being said, compared to other Gen 5 mons, they still do evolve pretty early compared to the rest of the Gen 5 roster.
Like, the only way I can at most see them try to circumvent that is by making them available "out-of-order", like the non-gen bird/bug/rodent coming halfway/later in the game and the pseudo being available early on...
Platinum Gible would like to have a word. Not to mention Goomy in XY is a mid-game Pokémon, and even way back in Gen 1 RBY Dratini can feasibly be obtained mid-game, possibly by the 4th Gym if you go out of your way to do so.
And even then, the gimmick of the pseudo-legendary isn't necessarily that they're always obtained late, but it's that they
evolve late and reach their maximum potential later than everyone else, but is super strong when they do, among the best in the game. All of them have the highest evo level of every mon in their generation, are in the slow EXP group, end up with 600 BST in their final form, and has a consistent catch rate throughout the whole line. Even though Gible is obtained early, it reaches its final form as Garchomp later than any Gen 4 Pokémon does, and in that context you will not have a fully evolved Garchomp until close to the 8th Gym in DP and Platinum. Most of the pseudos are a long and tedious grind, and you won't get their fully evolved forms until the very end of their debut games or close to it otherwise, close to when you're ready to face the Champion.
As for the others, having a bird/bug/rodent showing up later would kill their place in the archetype in the first place. Their whole schtick is that they're obtained in the first few routes.