As it patently was on the WCML when years of widescale disruption was caused just to clean up a few pinch points. Traffic on the route has grown another 30-40% since then which is why the better (and cheaper) solution to accommodate the continuing trend of growth is to create two additional tracks between the stations that the fastest services stop at. Because of the
much higher cost of working on a live railway (this particular one is the busiest main line in the UK), and the considerable disruption to those using the line and those living near the upgrading work, the overall cheaper option is a new alignment between the stations needed.
As far as Thameslink is concerned, there isn't a viable virgin route anywhere between West Hampstead and East Croydon, that allowed connections to central London locations, - there isn't a path even underground. A Thameslink service that couldn't stop between those two stations would be entirely wasted.