It leads straight to influencing a conveniently small group of people with other means. If you follow US politics even remotely, the term "pork (barrel)" should be enough to convince you that local representation is a bad idea. Clientelism is also easier in smaller electoral areas. Now add both.

In proportional representation it is still possible to vote for a local candidate, depending on how it is organized. Voting for a party is the common thing, but allowing people to vote explicitly for a candidate lower on the list allows getting a local candidate straight into parliament. Not that that is ideal, but it is definitely not impossible.