A subnet mask of 255.255.0.0 (/16) allows for more hosts on an IP subnet than 255.255.255.0 (/24). You don't actually have to put 65,000+ hosts on a /16 subnet, but you can.
Realistically, if you did put 65,000+ desktop hosts into the same subnet, the amount of broadcast traffic generated during the course of normal network computing activity could actually impact the processing power of each computer on that subnet. That's because each computer has to interrupt what it is doing to listen to the broadcast and determine whether it's something they need to pay attention to or not. (Most of the time the answer is "not".) The more computers each has to listen to broadcasting, the less CPU time the computer has to actually do work.
Computers with faster CPUs might not notice it as much, but slower computers can be significantly impacted by excessive broadcast traffic. It used to be that you could demonstrate excessive broadcast traffic as a problem by running a CPU-intensive desktop application locally: benchmark the performance somehow, while the computer is on the LAN; then detach the computer from the LAN and run the same benchmark again. If it runs faster OFF the LAN, then being on the LAN is actually causing performance degradation. And almost always this was the result of vigh volumes of broadcast traffic. (Sometimes it could also be a focused Denial of Service: depends on whether multiple machines/users on the subnet report the slowness, or only one.)
Smaller subnet masks like a /24 limit the number of hosts that can be impacted by broadcast traffic on a subnet. (Unless you support multiple /24 subnets layered onto the same Ethernet broadcast domain using "secondary" IP addressing on the same router or L3 switch interface. In which case performance problems are more likely to be caused by the bottleneck of routing from one subnet to another, in and out on the same interface. The fix here is to either break out each /24 to a separate broadcast domain/VLAN, or come up with an aggregating mask like a /22 or /23 that lets the hosts talk to each other directly across the broadcast domain, rather than funneling in and out of the router's interface.)
Having large subnets like a /16 can be a problem for routers when that subnet is the target of an intensive sequential IP address scan. You can have a Denial of Service on that subnet when the router interface involved has to ARP for thousands of unknown IP addresses and wait to see if anything responds. All that ARPing and buffering ties up router CPU and memory resources, and can result in severe performance degradation. With smaller subnets like a /24, you can mitigate the impact such an attack can have.
