Admittedly this report is from 2011, but it was the first I could find, and the figures likely haven't changed drastically:
For Euston specifically, only 20% of arriving passengers then walked to their destination vs 53% using the underground. A further 20% used either bus or rail for onward journeys.
One of the reasons for having two London stations was that if all HS2 passengers arrived into Euston it would overload the station. Even with Old Oak Common, there was concern that Euston would still be at or over capacity because of HS2 unless Crossrail 2 is built.
If Euston without OOC couldn't handle all HS2 passengers, it's fair to assume OOC without Euston couldn't handle all HS2 passengers. Both stations are needed and OOC will be quicker for HS2 passengers travelling to/from anywhere along the GWML or the Elizabeth line.
Travelling from OOC to Canary Wharf will take about 20 minutes on Crossrail with no changes, whilst Euston to Canary Wharf is 25 minutes with a change. Given a passenger getting off at OOC will get off the train say 5 minutes before a passenger getting off at Euston, that's 10 minutes quicker travelling via OOC. Whilst not a massive difference, it would be enough that the majority of passengers making the journey to Canary Wharf would do.
With regards to Heathrow, the spur option would never have worked. It would either require trains to route via Heathrow, thereby reducing the time saving of travelling to London, or would require dedicated trains to operate to Heathrow avoiding central London altogether, the demand for which would be too small to justify.
If including Heathrow in the High Speed network was so important, then routing the line itself from Euston to Heathrow then North would have been the best option, however failing that, the interchange at OOC is the next best option.