Are we getting a little carried away with expounding the perfect circuit and entry here? Yes they are possible, no, they don't happen often. I have no idea what happened here, other than the reported outcome.
We are best reminding ourselves about the need for ever vigilence for traffic. Much more than that, in terms of enless armchair investigating for an accident like this, I cannot see as being helpful. We must remind ourselves that all aircraft have blind spots, and it is always possible to have zero relative motion traffic. I had one a month or so ago, just one bug spot on the windsheild getting bigger, where the others were not. Head on. By the time I believed what I was seeing, it was time for quite an evasive turn. I don't think I was seen at all by the other aircraft - it never altered course.
Let's not beat up on ATC. They, more than we pilots, are bound by the procedures of their jobs. They do what they are supposed to do, and are not supposed to offer other services, not matter how temping, or well meaning. I'm sure there is a Shoreham controller who feels terrible. Let's support that person. We pilots have all of the opportunity for collision prevention, by any means, and the most interest in success too!
As for
What was the reason for the steep rate of climb?
Ooo, Ooo.... Ooo, I know this one! Because he could! I've done it, when I was flying a capable aircraft. Who among us would deny doing it!
I've flown from Shoreham (thank you, friend). There is a lot of "detail" on the ground all around there. That can make a small relative motion "target" much more hard to spot as traffic - it just blends into the background. Vigilence!
Perhaps there was fault, perhaps not, perhaps we'll never know. Just sad, and a reminder for us to follow patterns other pilots will anticipate, and keep our eyes open.