Basic question about transaction verification
My question is, if that is the case, why can’t the verification only check against transactions signed by Alice, why does it have to check against the entire blockchain?

A node has no concept of who controls certain outputs. So there is no way to 'check all of Alice's outputs', how would the node be able to ascertain which outputs belong to her?
Rather, the normal operation of a node is to check all transactions, to ensure that no transaction has spent coins that were previously spent (and to check that new coins aren't being created against the network's rules, etc). In doing this check, the node creates an index of unspent transaction outputs (UTXOs), which it will use to help check validity of new transactions.