The general rule is 9216 in the network devices (swicthes and routers) and 9000 in the server side, just because some operational systems doesn't support mtu greater than 9000. Another reason to leave the mtu bigger in the network is because the packet coming from the server side could be encapsulated by some protocol (VxLAN, NVGRE, Tunneling, etc.).
Why the ping doesn't work with 9000 packet size?
This packet size configured by the ping, is without the header, when putting the header (IP 20Bytes + ICMP 8 Bytes = 9000 - 28 = 8972) in the packet the server interface can't forward it without fragmentation.
The application usually do not control the mtu, this is a S.O. function, if you are using UCS you can configure the MTU there or also overwrite by the S.O. installed (not recommended). Few very specific applications are different.
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