Compared to a car or taxi it doesn't.

I guess we all have different definitions of best. Personally I'd much rather take a 15 minute train (leaving every 15 minutes) to the centre of London then a connecting tube (total £25ish, 30 mins) than sit in a taxi for at best half an hour, and often much longer, at a cost of £50-£100.

Of course, depending on timetables/connections the train could be a bit slower, and if one has a lot of luggage door-to-door by taxi might be better. But for me it would be hard to argue that fighting through London traffic in a car or taxi is superior to public transport.

I've traveled between core London and Heathrow many times, and every time I've taken the train, I've had a faster, more pleasant experience that I would have had in a taxi. Maybe it's different if you're heading to Heathrow from outside Zone 1.