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So pic related illustrates that skill specialists have no inherent potential that is realised with level. This is with the map set to OGPP so Grepa Berries are double strength, all Pokémon are baseline with zero boosts, main skill level 3 (from 2 evolutions) and mono-ingredient for consistency.
Note that Luxray's main skill (Cooking Power-Up S) cannot have its strength measured, but for the example it's the only fully evolved electric type ingredient specialist in the game.
Raichu from 10 to 30 only sees about +4.2k in berry strength gains, but 30 to 50 grants +6.6k and 50 to 60 alone grants +5.2k.
Raichu's gains from ingredients or skills are much lesser in comparison.
Luxray from 25 to 30, sees daily ingredient counts rise from 23 to 40, and is about +2.3k gains. From 50 to 60 this rises from a count of 42 to 57, and gains of +2k.
Ampharos from level 10 to 60, Charge Strength M usage increases from about 2.66 times a day, to 2.95 times a day.
Its daily increase in skill-based strength gains only goes from 4.6k to 5.1k (+0.5k), that's pathetic.
The other 10k in gains it realises are by a majority in berry gains, and ingredient gains are still 3x more than skill gains.
Also to note from this is that recipe levels exist; the more a given dish is cooked, the stronger it gets.
There is no equivalent there for skill specialists. It brings to mind the Move Levelling system that was introduced in Pokémon Mystery Dungeon: Gates to Infinity; where continued use of a Move improves that Move's Power, Accuracy, and PP for all Pokémon.
If Main Skills had this sort of perk, skill specialists would have more of an innate growth, and co-ordination of Pokémon by their main skill would have increased value (your berry or ingredient specialists all sharing Charge Strength S suddenly matter).
