OK, so here is my take on Alli. He is a player you need to structure a team around to get the best from him. We do not have the luxury at the moment to do this.
He is not going to run the distances that Iwobi and Gordon have done - but that is what we need at the moment.
I think Bill thought he was getting a bargain from his mate Levy (and it yet might be) and Spurs needed to free up the wages for Kulesevski and Bentacur which is why the timing worked for them.
Lampard was probably asked during his interview, "could you work with Dele Alli" as Bill would have had the deal lined up already. So he said yes (and he probably can in time), but his deal is basically Bill's last hurrah at a bargain. There is no way Lampard went into his interview saying "I need Dele Alli to stay up". Evidenced by the fact that he isn't playing him.
I believe he will be a good addition in time for us in time, but it is a question of expectation at the moment. He is a gamble, but one that could help us balance the books in the future - we just can't give him the time he is going to need or alter tactics to suit him until next season.
The problem is we all expected signings that would help our current situation immediately, but that is what Alli is. He is a longer term gamble. Once you get your head around that (annoying as it is), then you realise to just forget about him for now.