I would suggest that, in most cases, your house is somewhere to live, and should not be added to your "equity" investments. A possible exception is if your intend to downsize.
I'd agree with both of those points, but to be honest, if it's available, then the 'downsize option' doesn't sound like too bad a Plan-C -
Plan-A - Internally-generated income (dividends or realised investment capital) is large enough and lasts long enough to maintain a long and happy retirement. This might include an element of over-supply that can be re-invested to create a larger 'income-buffer'
Plan-B - Cash, or near-cash reserves are available that should last a relatively small number of years should an extreme market-downturn occur, where dividends or equity-prices experience large falls. Hopefully dividend payments and equity prices would regain most of their falls before these reserves are depleted completely, allowing more normal service to resume and Plan-A to be picked back up.
Plan-C - Rather than have too much in terms of cash, or near-cash reserves (which might simply be a level of cash that takes too long to generate, meaning retirement might be put off for some years...), having the option to release built-up equity in a house, and downsize to a smaller home, seems to be a useful option to have as a Plan-C, in the absence of a more appropriate 'Plan-C' solution.
Personally, I think there would be a great deal of belt-tightening if Plan-A were to struggle due to a market-downturn, which would hopefully serve two purposes -
1. Prolong the need to activate Plan-B.
2. Help, as much as possible, a move into Plan-B depleting my cash-reserves as slowly as possibly, thus reducing the chances of Plan-B being fully exhausted, and hence not even opening up the possibility of Plan-C being needed at any point.
But still, possibly having large amounts of equity in a home can be useful in the mix, when considering the potential options, and certainly if someone might consider the alternative might be to carry huge amounts of cash or near-cash in Plan-B, without considering the possibility of such a Plan C option......