That's not the plan which was being discussed here. See the post which started the discussion about reporting the Piccadilly Line:
OK to address
@Central 's specific point, no this is not correct, there is no plan for the District (I typed Piccadilly here originally - doh!) line to take over services to Rayners Lane and Uxbridge.
If memory serves, there was a comprehensive study of all the options to change services around at the West end of both the District and Piccadilly lines around about 2008-2009, just prior to the Subsurface upgrade) to understand what if anything could be gained from any of the options to change how these worked (options that have been talked about throughout my as a Transport Planner and no doubt were talked about by my predecessors and will be talked about my successors). There are a number of options that at first glance seem operationally more efficient, or at least address a particular issue (such as compromised height platforms) - playing around with District services to Edgware Road was one that repeatedly came up.
These options were all evaluated to understand their impact on passenger journey times, passenger numbers and costs. Almost all of them create more losers than winners among potential passengers, such that even ones that did reduce cost, ended up losing even more potential revenue. This is unsurprising really, people tend to find places to live with more convenient links to where they work - break more of these convenient routes than improve from the change and you tend to increase interchange and thus journey time. Of course over the long term, people would find different places to live, but this immediate disbenefit creates a lot of 'inertia' and explains why routes rarely change once established.
However the study did find one exception. More people would gain from a change to the Ealing Broadway service than would lose. The key winners are District line passengers on the busy Wimbledon and Richmond branch, whose frequency would be increased in a way that is hard to do any other way, as there are no spare paths beyond the 32 tph envisaged at the end of the Subsurface Upgrade. However the Piccadilly line upgrade envisaged 36 tph, which meant that significant increases on the busy Heathrow branch could still be made with 6 tph going to Ealing Broadway (that 6 tph would probably have ended up as Northfields reversers anyway). So more people gain, than lose (mainly passengers from Chiswick Park to Ealing Broadway wanting exclusively District line destinations). Since that study, upgrade plans have been in line with this envisaged end state.
The study looked at, but rejected an entirely or partially District service to Uxbridge and Rayners Lane, but to replicate the existing peak frequency on this corridor (12 tph) with District line trains would require a reduction of the service to Wimbledon and / or Richmond, or would end up with large numbers of High Street Kensington reversers which are much less useful than through trains to Central London. Added to this the S Stock fleet is now long complete and the type out of production with nowhere near the numbers of trains that would be required to support that option.
The London Reconnections article added to
@Enthusiast 's post #38 above covers much of this. The '2024' map however is a bit premature...