I'm beginning to wonder if anything you write is ever serious, Craig. To some it might appear that your only interest is to have a silly argument as often as you can.
Please let me know when I'm patronising you, but I'm going to spell this out really, really simply in short words:
If Labour goes left it will not get elected. If it doesn't get elected, the left in Britain will be less well represented in our national discourse.
Following so far?
So, if Labour wants to represent the left effectively, they also have to appeal to left leaning centrists, otherwise they (Labour) will remain permanently in opposition. Labour being permanently in opposition does no-one any good, and would make for poor governance of this country.
Similarly, on the other wing of UK politics, the Right. If the Conservatives move too far to the right, they will be unelectable (presuming this doesn't happen at the same time as Labour are hard left). If the Conservatives sit on the opposition benches for too long as a result, those with a right wing agenda in this country will similarly be frustrated by their lack of representation or power. Therefore, if the hard right want adequate representation in government, they have to accept that the Conservatives should be a centre right, rather than a hard right party.
Relative extremism on either wing results in time out of power, to the detriment of the very people who are most closely associated with the more extreme views. Is that clear now?
I suppose the question that Labour need to answer is whether, to appeal to the centre-ists (and maybe not just the left leaning ones, there may not be enough of them) they have to adopt policies which not only make them functionally indistinguishable from the Conservatives but mean that they fail to attract the core voters who don't solely vote on the basis of party loyalty.
It's comparatively easy to imagine a scenario where, to establish their financial credentials they "out Tory" the Conservatives when it comes to austerity measures, ensure their military support by increasing defence spending and show that they're not soft on crime by introducing draconian laws.
There's a stage where they're no longer anything other than the Conservatives. IMO Blair with PFI regularly overstepped the line and was, in effect, a Tory prime minister.