If on a router is defined a static route using as gateway one of its interfaces instead of next hop IP@, then my understanding is that Proxy ARP is mandatory to be enabled on the remote router connected to that interface, otherwise that remote router won't reply to ARP Request sent by this router.
Am I right?
Ex: if on router R1 I define a static route as follows:
ip route 188.8.131.52 255.255.255.0 fastethernet 1/0
then on router R2 connected to that interface proxy arp is mandatory to be enabled.
your understanding is correct when you specifiy an outgoing interface of type ethernet for a default static route your router is relying on the willingness of another device to answer to arbitrary ARP requests (on proxy-arp indeed)
I saw this in a customer network: some c7200 were acting as L2TP terminators of access services and they had
ip route 0.0.0.0 0.0.0.0 fas0/0
after a security assessment the ip proxy-arp was disabled on the router they were connected to and as a result of this service stopped to work.
fixing the static routes using ip address as next hop solved the issue.
on a windows pc if you specify the ip address of the PC itself as its default gateway it will rely on proxy-arp as a router with a default static route that specifies the interface.
There is another thread where high cpu and memory usage is caused by this type of default static route.
Hope to help