Hi @Alice,
Welcome to the community forum 
I am not keen on approving a maximum as an allowance for ERC20 nor semantic overloading. Interested to learn other use cases.
I had a quick look through the List of Solidity libraries in the wild to see if any had a max uint256 constant.
OpenZeppelin Test Helpers have JavaScript constants such as MAX_UINT256. If there are use cases and a need then there would be an argument for adding common constants to OpenZeppelin Contracts.