We have the third highest wage bill in England, I agree. However over the past few years our spending on transfers has dropped massively, because transfer fees are now significantly lower (pro-rata) than a decade ago, but we haven't upped our wages to compensate.
Our wage bill is probably only £25m behind Arsenal's (less if you discount trophy winning bonuses which obviously Arsenal don't have to pay!), despite our profits being roughly £65m a season more. This taking into account that Arsenal are renowned for being an incredibly tight run ship.
Usually you'd expect if the value of transfer fees halves, the wage bill would go up % wise (because clubs are taking less money, therefore the player would take more).
In answer to your question, you need to treat modern day Footballers as employee's and not fans. If I was an incredibly gifted (for instance) sales person and a 2 companies tried to poach me, money would be a big factor in where I decided to go (not the only factor, but a big one). Why the hell would and should the likes of Silva/Aguero/Toure etcetc take a pay cut to join one company over the other. In fact I would turn it around, it is implied that the company offering more has a higher opinion of your abilities and more faith in you than the company offering less.