Take clean zabbix_agentd.conf, and read documentation that EnableRemoteCommands is deprecated

This parameter is deprecated, use AllowKey=system.run[*] or DenyKey=system.run[*] instead.

Add:

AllowKey=system.run[*]

See warning
zabbix_agentd [141208]: Warning: key access rule "system.run[*]" conflicts with another rule defined above
Test if it works:

zabbix_get -s 127.0.0.1 -k "system.run[echo 2]"
ZBX_NOTSUPPORTED: Unsupported item key.

For some reason it says unsupported item key but made sure that key is correct so it is not allowed

Try deleting DenyKey
See error:

zabbix_agentd [141243]: ERROR: "AllowKey" without "DenyKey" rules are meaningless

What can be done to enable remote command ? Documentation states simply

use AllowKey=system.run[*] or DenyKey=system.run[*]

So it looks like we need to add at least something to DenyKey ?
Add:

DenyKey=test

See:

zabbix_get -s 127.0.0.1 -k "system.run[echo 2]"
ZBX_NOTSUPPORTED: Remote commands are not enabled.

Still not working, how to enable remote commands there is only one option to do that but it is deprecated.
OK, try to use nevertheless

EnableRemoteCommands=1

See warning

Warning: EnableRemoteCommands parameter is deprecated, use AllowKey=system.run[*] or DenyKey=system.run[*] instead

But got it working

./bin/zabbix_get -s 127.0.0.1 -k "system.run[echo 2]"
2

Expected:
Documentation and logs must not be so misleading and it must not be so hard to enable remote commands and it must be possible to enable remote commands without deprecated option, please provide example at least.