I look at what you get at Hayes, even in the most ideal world, and the maximum is probably 8tph. That still precludes Beckenham Junction, and if you are living in some parts of the world near there, to go to Beckenham Junction and have that other onward connectivity (especially as this would surely make Beckenham Jn a stop on fast trains finally), is massive.
And of that heavy rail 8tph, even if its 4tph fast to Charing Cross, and 4tph via Lewisham to Cannon Street, and you still miss a lot. To be able to get to somewhere like New Cross Gate, which is a gateway to East London and also the likes of Crystal Palace (that bit more important for people getting out at Lewisham, going to the Bakerloo, and getting to NXG which they can't do now), is huge. To then have Elephant & Castle and the Thameslink and Northern lines, is equally positive.
You get to Waterloo and Charing Cross, and your journey time has probably barely degraded, but the frequency is the selling point. As you say, you're not now trying to go down into the Tube at those places for Piccadilly Circus, Oxford Circus, Baker Street and Paddington: you're already on the train. Journeys to Heathrow Airport become massively simpler.
I didn't live on the Hayes line, I lived on another Metro route out of Cannon Street / Charing Cross. But if I did live on the Hayes line, I'd be all over this. Look at what Crossrail did for London, and then imagine what this whole project does along the Old Kent Road, through those parts of 'South Bermondsey' and 'North Peckham'. Even at New Cross Gate, it removes probably 50% of people coming up on the Overground from South London, giving that vital capacity in the core section of the ELL from Surrey Quays to Dalston.
For Lewisham, and therefore the wider South Eastern metro area, it's just as big. All those flats, now getting a proper Metro service. Catford station reunited (you hope), Beckenham Junction actually getting meaningful connectivity to places like Lewisham or up to the East.
It's hardly needing to be sold. It's just got to be done.