Not a very surprising finding. The loudest parts of the system are all outside the very centre (i.e. Circle line), i.e. where the trains run the fastest.
I don't think one can make that connection at all. The Victoria Line runs at a pretty constant 50 mph from end to end, including through the centre. The Jubilee reaches 60 mph between Baker Street and Green Park. Even the humble Northern Line, not really known for speed, reaches 47 mph on the short hop between Warren Street and Goodge Street!
Some of the sections highlighted for noise, e.g. Camden to Euston s/b, Kentish Town to Tufnell Park n/b, are only 35 mph. Lambeth North to Waterloo is hardly fast!
The noise itself seems to be rail roar and it is worse on the ATO lines where near identical acceleration/speed/braking patterns of every train contribute to railhead wear that creates the noise.
I'd say there are two issues. Firstly the amount of rail grinding going on has very much increased in recent years, just like on the mainline, which produces a high-pitch whine which is even more noticeable in the tunnel environment. Secondly, there have been some changes to track formation on some specific curves. It's very noticeable that at least two of the noisy sections (Euston/Camden and Kentish Town/Tufnell Park) coincide with this. I have a feeling this was done as part of the preparations for Night Tube, perhaps as a vibration mitigation measure. Whatever the reason, I think it's more specific than just due to rail wear.
The Metropolitan was obviously the quietest of all lines as over 85% ia above ground and most of the subsurface running is in twin track tunnel and at relatively lower speeds.
Still reaches 45 mph in the tunnels, but perhaps brick absorbs noise better than other materials? That is when the Met isn't running "stick to stick", of course, which is much of the time.