Gym leaders change teams based on the opponents level. I don't think Falkner would use Pidgeot against a starting trainer with Chikorita. There are other examples like Winona and her Skarmory plus Volkner and his Raichu.
While Korrina did use her ace in the match and went all out.
I actually think Falkner would use Pidgeot against a starting trainer with Chikorita, but only if said starting trainer knocked out both Hoothoot and Dodtrio first, then Falkner would just use Pidgeot as his final Pokemon like he did with Ash. It would also be very likely that the starting trainer would lose to Dodrio without ever seeing Falkner's final Pokemon. In this scenario, the starting trainer would lose
at least 2 or 3 times to Falkner before finally getting a badge, assuming they didn't just skip Volkner to challenge an easier gym and/or completely give up their journey (like the other 2 trainers from Pallet Town other than Ash and Gary).
Gym leaders only change their teams according to the opponent's levels in the games, and also in Origins (which is based on the games). In the actual anime, we see that the gym leaders always go all out (barring rare exceptions) in matches, using their ace Pokemon. The most notable example was Elesa sweeping Bianca 3-0 with one Pokemon, and this one is interesting since its the only time we see a gym leader sweep someone 3-0 on-screen. A minor example would be Clemont using his ace Luxray to beat Sawyer who only had
at most 2 badges (possibly even no badges), in what was very likely an off-screen 3-0 sweep. Also, basically every gym leader except Volkner used their ace Pokemon against Ash.
Ash vs Korrina had the added bonus of Korrina not just using her ace Pokemon, but actually using Mega Evolution against a trainer who couldn't Mega Evolve their Pokemon. Korrina's Mega Lucario would beat most of Ash's reserves in a 1-vs-1 battle pretty handedly, and even Base Lucario would still beat several of Ash's reserves 1-vs-1. The idea that gym leaders hold back against challengers according to their badge count is mixing up the anime with the games (and by proxy, with Origins). The instances of a gym leader handicapping themselves are exceptions, not the rule, and are usually pointed out in-universe (e.g. Ash vs Roxie).
Even with Volkner, its still possible (but admittedly unlikely) that Raichu was formerly Volkner's strongest Pokemon many years ago in his past, but not during DP. Obviously, its still a massive of holding back since Raichu should still be above Electivire or Jolteon. It might Volkner's 'main' Pokemon but it doesn't have to be his current ace, similar to how Ash's main Pokemon (Pikachu) is arguably not his consistently strongest one (Charizard). Either way, Volkner holding back with Raichu is the exception to the norm.