"Yes, many other departments make demands, but do NOT bother to take them time to sit down with the IT people and work out what is possible within all those constraints."

It's incumbent on IT to provide options, not the business to beg for them. And again you have spent time railing on about the cloud and BYOD rather than looking at how to provide the services needed without the downsides (and options exist for all of the issues you listed). I'm not talking about always saying "yes", but about helping them get what they need within the system rather than saying "request denied".