I would say that a flat network would allow any traffic to any workstation or server. I think that with 1000 users, a routed network can be good since you will have better control about where people are sitting. It is easier to keep a structure in your network especially when you say that people are spread over 10 buildings. Furthermore you can add some security on the routers and have a better control over different flows.
As Narayan has said there are certain broadcasts that you just wouldn't want to block. Arp is a case in point. Without arp you would have to manually enter every mac address on every device which is not pratical with a thousand hosts.
A flat network with 1000 hosts would mean every arp/DHCP/broadcast app request would have to be processed by every machine.
In addition as other poster said routing allows you to impose some sort of hierarchy on your network, filter traffic between vlans, apply different rules to different vlans etc.
The previous posts have given good reasons for routed networks, especially when you have the geographic separation that your environment seems to have (10 buildings). I would like to point out what I believe to be a logic flaw in the original question. As I understand the original question asked: "with broadcasts blocked at the switches". But switches (at least layer 2 switches) do not block broadcasts. And if the original question was asking about layer 3 switches blocking broadcasts then it is assuming a routed network instead of a flat network. :)
Although that is correct that you cannot have a L2 switch that can block broadcasts, you can have a device that bridges two networks and acts as a firewall to block certain broadcasts. It does not have to be routed. This is what they were trying to do.
We are pleased to announce availability of Beta software for 16.6.3. 16.6.3 will be the second rebuild on the 16.6 release train targeted towards Catalyst 9500/9400/9300/3850/3650 switching platforms. We are looking for early feedback from custome...