The 0757 5-car Heathrow Connect from Heathrow to Paddington was already No 4 in the official list of "most overcrowded trains in Britain". Trains on this line are already stuffed, on operations which into other London termini would have 10- or 12-car sets. GW seem incapable of providing more than the minimum capacity, standing in minimal formations off-peak or (particularly) at weekends is common.
Could you enlighten us as to where GWR is supposed to have got more rolling stock from? Once electrification was on the way, the idea of acquiring more dmus for FGW, which was quite well advanced, went by the board. Instead, they had to bring back the five 180s they could get their hands on and acquire the two 150/0s to free up as many Turbos as they could to strengthen Thames Valley services.
I don't recognise this 'minimal formations' stuff. You might have had a point a few year ago when many peak trains at Paddington were just three-car sets but there are plenty of 2+2, 2+3 and 3+3 Turbo formations these days, never mind HSTs working outer-suburban semi-fasts to free more Turbos for those coupled formations. That's not to say there isn't a problem with overcrowding, there is, but GWR are doing the best they can with what they have to hand for the suburban services at the moment, which is a fleet ordered almost 25 years ago when you would have needed a very good crystal ball to predict the demands on the Turbo fleet these days.
Pretty much as soon as the first emus arrive, GWR will be pressing them into service out to Hayes & Harlington once staff are trained to operate them, precisely in order to boost capacity.
So
that's where they come in! It all makes sense now
This and also the fact that trains over 5 cars in length are badly needed on GWR anyway. It seems like all the suburban trains coming out of Paddington are full and standing no matter what time of day it is.
How many people do you think use the Greenford service - the clue is the size of the trains that operate it... The key job of the emu shuttle to Hayes will be to provide an instant boost in capacity for the inner suburban mainline stations where the Turbos and Heathrow Connect desperately need help.