Understanding Proxy ARP and the difference between routing to an interface and routing to next-hop

When routing to an interface, the router performs layer 3 to 2 resolution on the final address.  When routing to a next-hop value, the router performs layer 3 to layer 2 resolution on the next-hop address.

In this lab, I will demonstrate the difference between routing to an interface and routing to a next-hop.

After performing a ping test to the Loopbacks, the ARP table is built.  Notice in the output of the ARP table, the 2.2.2.2 destination is in the ARP table, but the 1.1.1.1 is not in the ARP table.

This is because R3 directly ARP for the address 2.2.2.2.  Since R2 has Proxy ARP enabled by default on its interface connected to segment, it will respond to R3's ARP request with its own MAC address.


What if we disable Proxy ARP on R2's fa0/0 interface:

On R3, we will clear its ARP table ('clear arp' will not clear the table). Notice that 2.2.2.2 is cleared from the ARP table.

Now, when we try to ping 2.2.2.2, we get:

Verification:
debug arp
debug ip packet

Question now is:
1. Why is this important design-wise?
2. What are the alternate solutions?