Does he have to 'improve us' ?
That implies we need to be getting better players than those we already have, but it's just as valid to swap out one water carrier for another, and possibly save some money in the process, or gain a couple of years in age etc. We also have the home grown issue to deal with, which can't be ignored. We HAVE to have more home grown - it's just a matter of where they come from and the price. Is anybody in the Academy as good today as Delph? if not, then we need to buy.
We don't know that Wilshere is even possible, but we do know his price would be pretty high. Same for the likes of Barkley. So Delph solves a problem at a sensible price. If / when we can upgrade on him, I'm sure we will, but until then, he plugs the HG gap with a reasonable skill level.