I don't know how you reached this conclusion. I used journey planning on TfL and it came back with the following timings for walking from the stations:

Forest Hill station to Willow Way = 20 mins
   

Sydenham station to Willow Way = 11 mins
   

Forest Hill station to Thorpewood Avenue = 11 mins
   

For completeness: Sydenham station to Thorpewood Avenue = 18 mins

To be fair, if you use the bus the timings are about the same, but no quicker than walking from Sydenham.

If coming by train they are likely to continue to two extra stops on the ELL to Crystal Palace and walk through the park (total time 19 mins). So it will actually be quicker to get to Crystal Palace pool by train than to walk to Willow Way!

As you pointed out in your previous posting, rather than a 20-30 minute walk people will use their cars. There is no parking capacity in Willow Way so they are more likely to go to a pool with good parking - The Bridge, Crystal Palace, or Beckenham. The Willow Way site is the wrong location. It is outside either of the defined town centres and has not parking capacity. This is contrary to national, London, and local policy for the positioning of a leisure centre. And for good reason, such a site for a leisure centre is not economically sustainable.

With regards to the live/work proposal, we are still preparing costing and a full analysis. In the current market it does not alone solve all the financial problems (but then neither does housing on the pools site fund Willow Way funding gap), but it does make a significant contribution and is actually a very interesting development in its own right. At this stage I do not want to give further details on a public forum as this is not the right place for proper consideration (it will be made public in due course).

And one other alternative approach is to find a way to build a pool on the existing site for less than ?12m. There are a number of ways to do this, all of which involve compromise in terms of design or facilities, but at least they give us a viable leisure centre.