Heather - I would agree the purpose of the cash transfer needs hammering down, but that doesn't just mean being precise about the purpose: we have to be exact about the ethical status of the transfer. Is the cash, itself, the object of the obligation (e.g. repaying a loan), or is the cash given in fulfilment of an obligation to a further end? - the latter arguably seems to me the case in respect of poverty relief, and if so the "does it work well" question seems pertinent. (these aren't the only possibilities, e.g. the cash could be a 'no-strings gift' or a 'gift with an explicit purpose')
Most contemporary moral philosophers who write on poverty agree, at least, that those able to help have a duty to do their fair share of alleviating extreme absolute poverty - there doesn't have to be a past wrong for there to be a moral obligation to, as you put it, "improve welfare now", and giving cash to poor people looks like one candidate for fulfilment of that duty in whole or part. The World Bank agrees that ending extreme poverty is an urgent normative demand, FWIW. Skipping a few steps, it seems to me that this could ground a good reason to assess "working well" by asking "is this effectively fulfilling our duties".
Let's make this purely about the donors for a moment. If I have a choice of ways to fulfil my obligation to the world's poor, then how effective each of those methods are is an important question for me. Without knowing this, I can't know how much of any of these activities I need to do - e.g. direct cash, loans, national/international political reform etc. - in order to do what I should. Depending on the resources at my disposal, and other morally significant things I need to do with those resources, it might well be morally preferable, or morally essential, for me to prioritise the most cost-effective activities.
There's a separate issue here that poverty, surely, doesn't neatly map on to a shortfall in (simple) welfare. Ideas like 'capabilities' or 'basic rights' do some work in - or reflect - weightings of different dimensions of multidimensional poverty. This is to some extent independent of the preferences of particular poor people, but I am not sure it is necessarily hubristic (though this is a danger).
I don't know if this helps?