Following the official Medalla launchpad at https://medalla.launchpad.ethereum.org, at some point you need to connect to a wallet and the only options are MetaMask, Portis and Fortmatic. Why is this so? Why can't I use Geth or similar?
My understanding is that the launchpad was made to be as user-friendly as possible, including for users who are less CLI-proficient. In the interests of making things as streamlined as possible, various options were not included. If you would like to research a more manual method for connecting to Medalla (using Geth, for example), the information you need should be accessible in the Medalla repo: https://github.com/goerli/medalla/tree/master/medalla
Some of the older repos inside the
goerli/medalla directory should have more details about the process of getting on an Eth2 testnet using the command line (including the Goerli deposit), see for example the Witti instructions for connecting Lighthouse using the command line or other resources in that directory - most clients connected from the command line then.
To answer your question directly, the wallets you mentioned are a convenient way for the Medalla Launchpad to allow you to send Goerli ETH to the deposit contract.
The Medalla launchpad helps you send Goerli ETH to the deposit contract. This means that you need a wallet (interface), such as MetaMask, Authereum, Portis, etc.
Geth is client software (written in Go). While you can use your wallet in Geth, most day-to-day users will have a wallet interface, as mentioned above. Geth is more for underlying infrastructure such as mining, peer discovery, etc.