Part you’re missing.
AOE2:DE is a respectable PvP game. It has exclusive factions/units, but whatever faction/unit you use functions exactly the same regardless of whether you’re playing Japan with only the base game or have all the DLCs.
League of Legends used to have P2W on par with Crew Skills. It was called Rune Pages. You’re encouraged to investigate and discover the sheer amount of controversy such a mechanic had in a “E-sports” game. Rightfully, Riot removed it and made players have access to all runes at level 1 with only access to more pre-set configurations being tied to progression/payment.
Dota2 is epitome of e-sport/PvP. You get full roster, you get zero out-of-match influence over what happens in-match. In Dota2, people even consider skins that change the colour AND silhouette of heroes potentially P2W due to glance value being impacted, giving a minute advantage as the opponent needs a fraction longer to ID your unit. There was a whole drama over adding a hat cosmetic to a red hero as it made him similar to another.
Overwatch is another example of a functional PvP game. It has bad design choices made that killed it, but it was actually player-skill oriented.
Team fortress 2 has “either buy or unlock” equipment. That equipment functions the same regardless though. Whether you’re a orange box owner or some random f2p, your rocket launcher will behave the exact same.
Mech Warrior Online has exclusive units/loadouts that are only obtainable by paying. However, non-exclusive loadouts perform exactly the same regardless of who uses it, provided equal skill and circumstance.
FF14’s PvP arenas use pre-built characters and pre-generated equipment to eliminate Out-of-Match influence over player skill measurement.
GW2 follows the same trend.