Is there any point in reducing non-playing staff wage bills?

I think the title pretty much says it all really.

Obviously, in real life the answer is: Yes!

However in FM it doesn't seem to be so clear.

For example - I have just become manager at a fairly cash-struck club.

I have £0 transfer budget and am £25k/wk below the wage limit.

I want to sign some new coaches - as it happens they are better coaches, with better reputations but that isn't necessarily the main issue at this moment.

The board will allow me to sign more coaches - and they will allow me to offer up to a maximum of £1k/w for a certain coach ("Coach A", for example).

However Coach A wants £2k/w.

It would be fair enough if the board had set a maximum limit for coaches - but why do they then allow me to offer £2k/w to a lesser reputed coach ("Coach B") with lesser stats, that will also require a compensation fee to be made?

This is illogical!

Even if I reduce my players' wage bill by a further £20k/wk I still can't increase my offer to Coach A.

Also, by terminating many backroom staff contracts by mutual consent and bringing (or attempting to bring in) staff at a fraction of their wages, I am effectively halving the wage bill of the backroom staff - so why doesn't this affect the wage budget for either players or non-players? And why can I still not offer more to Coach A?

In FM is there any point in reducing the staff wage bill? In the short term at least?

What are the pros and cons I'm surely overlooking here?

And if staff wages don't come out of the wage budget, then why do compensation & fees to sign staff come out of the transfer kitty?

Staff wages do come from the wage budget, and it makes sense that compensation (like a transfer fee) for staff you sign should come from your transfer budget. But I am 100% with you that the board limits are inconvenient, because often there is an artificial wage ceiling for coaches even though I have lots of room in the budget.