I hate to break it to you, but you misunderstand the difference between layer 2 vs. 3, bridging vs. routing and how ARP works.
In your scenario where LAN clients only see the MAC of the Access Point, the AP is acting a a Router (Layer 3). A bridge works at layer 2, all MACs are passed unchanged. A bridge is nothing more than a two port switch (or hub, depending on how/if it manages unicast/broadcast/multicast). This has nothing to do with the nature of wireless.
Even if the AP is acting as a router as most home APs do, having identical MAC addresses on the wirless side will still mess with ARP and cause all kinds of weird connectivity issues. Even in the best case where you've spoofed your target's MAC address *and* IP address, there will be no way to differentiate which packets from each machine go where. In an unswitched network, you'll get massive collision errors and TCP will be quite upset with incomplete conversations flying around and in a switched environment, the switch's MAC table will be FUBARed.