Because you’re on a PVP realm. This suggested method wasn’t introduced until late Retail WoW with PVP War mode which doesn’t exist in Classic - which is entirely divided into PVP and PVE realms. You chose to enter a PVP realm.
On PVE realms though disabling the PVP flag will not flag you for PVP until you enter instanced battlegrounds or red zones or attack flagged toons. That is exactly the content you’re seeking.
Yes, this is the very solution that is offered to you: A FCM that is randomly unlocked and given from PVP to PVE realms.
They would have to consider doing this not only for this but everything that involves a PVE aspect in the game, while you enrolled into a PVP realm. The easier solution is to allow you to move from a PVP realm if you do not wish to do PVP.
After opening the shop, a token will appear with “Free Character Transfer” with a warped portal that is different from the other tokens to the paid services.
Please be aware that PCT is not available for Seasonal realms.
While the in-game shop is available in the WoW Classic client, Blizzard does not have the ability to disable it for specific servers (such as SoD realms).