Edit 2:
As you mentioned...
ip route 10.1.0.0 255.255.0.0 iface0
Forces the Brocade to proxy-arp for every destination in 10.1.0.0/16 as if it was directly connected to iface0.
I can't respond about Brocade's ARP cache implementation, but I would simply point out the easy solution to your problem... configure your route differently:
ip route 10.1.0.0 255.255.0.0 CiscoNextHopIP
By doing this, you prevent the Brocade from ARP-ing for all of 10.1.0.0/16 (note, you might need to renumber the link between R1 and R2 to be outside 10.1.0.0/16, depending on Brocade's implementation of things).
Original answer:
I expect that in most, or even all, implementations, there is a hard limit on the capacity of the ARP table.
Cisco IOS CPU routers are only limited by the amount of DRAM in the router, but that is typically not going to be a limiting factor. Some switches (like Catalyst 6500) have a hard limitation on the adjacency table (which is correlated to the ARP table); Sup2T has 1 Million adjacencies.
So, what happens when the ARP cache is full and a packet is offered with a destination (or next-hop) that isn't cached?
Cisco IOS CPU routers don't run out of space in the ARP table, because those ARPs are stored in DRAM. Let's assume you're talking about Sup2T. Think of it like this, suppose you had a Cat6500 + Sup2T and you configured all Vlans possible, technically that is
4094 total Vlans - Vlan1002 - Vlan1003 - Vlan1004 - Vlan1005 = 4090 Vlans
Assume you make each Vlan a /24 (so that's 252 possible ARPs), and you pack every Vlan full... that is 1 Million ARP entries.
4094 * 252 = 1,030,680 ARP Entries
Every one of those ARPs would consume a certain amount of memory in the ARP table itself, plus the IOS adjacency table. I dont know what it is, but let's say the total ARP overhead is 10 Bytes...
That means you have now consumed 10MB for ARP overhead; it still isn't very much space... if you were that low on memory, you would see something like %SYS-2-MALLOCFAIL.
With that many ARPs and a four hour ARP timeout, you would have to service almost 70 ARPs per second on average; it's more likely that the maintenance on 1 million ARP entries would drain the CPU of the router (potentially CPUHOG messages).
At this point, you could start bouncing routing protocol adjacencies and have IPs that are just unreachable because the router CPU was too busy to ARP for the IP.
Your reasoning is the wrong way. TCP/IP handles the layers top down, not bottom up.
PC A will first do a lookup in the routing table and decide that the only way to reach PC B is via the router specified in that routing table.
If the MAC address of the router is unknown it will send an ARP request to figure out which MAC address corresponds to the gateway IP.
Then the frame (containing the IP packet) will be sent to the MAC address of the router which will do a lookup in its routing table to see on which interface PC B is connected or via which next hop it should be routed. Assuming PC B is connected to another interface of the router the router will do a lookup (and if needed an ARP request) to figure out the MAC address of PC B and then forward the frame.
Best Answer
ARP is required when an IP packet is forwarded over Ethernet. When the IP address is in the local subnet it'll be ARPed, the IP packet wrapped into an Ethernet frame addressed to the ARPed MAC address and sent out.
When the IP address is not in the local subnet, another router is required (next hop), so the frame is addressed to the router's MAC address instead (which also requires ARP first).
Of course, not every IP packet triggers an ARP request - ARP responses are cached for some time ('ARP aging').