Waterloo was looked at when the HEX was being planned years ago. But the really fast 4-track lines into Waterloo don't run anywhere near LHR as they head out through Surbiton / Wimbledon to Woking. The nearest line into Waterloo from LHR is a twin-track suburban commuter line from Staines with stations every few miles. Would not really be a Heathrow "Express" to have linked that line.

In contrast, just to the north of LHR runs the high-speed 4-track GW lines into Paddington so this was the obvious answer to create the Express line into central London. But as you point out, Paddington is not really central, although the west-end can be reached in about 15 minutes on the Bakerloo line.

Then we had the "Airtrack" plans to link LHR to Reading and Waterloo (albeit it would have been a slow stopping service) but these plans were finally abandoned a couple of years ago