The attraction is latency: fewer hops between the client's system and the matching-engine. The historical problem was naked access, where clients connected with no broker controls at all, so a client software failure hit the market directly.
The market-access-rule banned that. Controls must now be under the broker's exclusive control, which in practice means a low-latency risk gateway the broker owns.
Example: a firm's servers sit in the exchange colocation hall and send orders through a hardware risk filter enforcing a 10,000-share maximum order size and a $5 million daily notional cap. Round-trip latency is perhaps 25 microseconds, versus 200 through the broker's full order stack.
Related: direct-market-access, market-access-rule, colocation, pre-trade-risk-check